Jacob Palis Jr

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15 March 1940
Uberaba, Minas Gerais, Brazil

Jacob Palis was a Brazilian mathematician who was a leading expert in dynamical systems. He gained many international prizes for his outstanding research contributions and also served as president of the International Mathematical Union as well as several other academies and societies.


Jacob Palis Jr. was the son of Jacob Palis Sr who emigrated to Brazil from Lebanon. Jacob Palis Sr married Sames, an immigrant to Brazil from northern Syria. Jacob Jr is the youngest of his parents' family of eight children, having four older brothers and three older sisters. Jacob Palis Sr had a large store in Uberaba, a city in the Brazilian Highlands, which sold everything. He did not let his children help in the store, however, since he was very keen that they should have the best quality education and all study at a university, this was his obsession. Jacob said in the interview [26]:-
When I was four years old, my parents enrolled me in a small school near my house. I would walk to school and back home by myself. When I went to the public elementary school, I already knew how to add, subtract, multiply and I knew the elements of mathematics.
Palis attended school in Uberaba then in 1956, when he was sixteen years old, he moved to Rio de Janeiro where he lived with one of his older brothers who by this time was studying engineering at the Federal University of Rio de Janeiro. Let us note that this university was called the University of Brazil at this time and only acquired its present name of Federal University of Rio de Janeiro in 1965. Palis's brother had a very comfortable apartment that faced the Sugar Loaf Mountain which is on a peninsular jutting out into the Atlantic Ocean. After studying for one year at High School in Rio de Janeiro, Palis sat the entrance examination for the University of Brazil. He was awarded the highest grade but was not allowed to begin his studies as he had not reached the minimum entry age for the University. After one further year at the High School, he again sat the entrance examinations, again was ranked with the highest grade and entered the National School of Engineering at the University of Brazil to begin his studies in 1958.

Although Palis was studying for an engineering degree, the subjects that he loved were mathematics and physics. At this time it was a standard route for those interested in mathematics to take engineering courses and mathematicians taught in the National School of Engineering. For example the mathematician Maurício Matos Peixoto was the professor of Rational Mechanics in the National School of Engineering and he strongly influenced Palis. When he was well into the engineering course, Palis began to attend talks at the Instituto de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro and also, but rather less often, he went to the Centre of Brazilian Physics Research (CBPF) in Rio de Janeiro. At this time Palis still intended to have a career in engineering but he planned, after gaining his engineering degree, to study mathematics and physics, then to return to engineering with the great advantage of having a very strong mathematical and physical base behind him. He graduated with his engineering degree in 1962 and then, influenced by Maurício Peixoto, he went to the Institute of Pure and Applied Mathematics (IMPA) as an intern.

At the Institute of Pure and Applied Mathematics he studied with Maurício Peixoto and Elon Lima. Peixoto had studied for a doctorate at the University of Chicago but had returned to Rio de Janeiro when offered a professorship at the University of Brazil without completing his Ph.D. studies. Elon Lages Lima (1929-2017) had been awarded a Ph.D. by the University of Chicago in 1958. Both Peixoto and Lima had met with Stephen Smale in Princeton in 1958 and were very impressed with his work on dynamical systems. They suggested to Palis that he should go to the United States and study for a Ph.D. on dynamical systems with Smale. Palis took the advice and wrote to Smale who was at that time at Columbia University in New York. With strong recommendations from Peixoto and Lima, Smale rapidly accepted Palis and agreed to be his advisor. In December 1963 he accepted a place at Columbia University to study for a Ph.D. beginning in September 1964.

The next major task for Palis was to obtain a scholarship to support his doctoral studies. In April 1964 there was a coup by the armed forces in Brazil which led to a military dictatorship. The National Council of Scientific and Technological Development which gave scholarships to outstanding Brazilians to study abroad ceased to operate after the coup and Palis feared this would put a stop to his plans. He had relied on financial support from his father through much of his education and felt there was no way to ask him for further financial support. Then somebody suggested that he apply to the Instituto Brasil-Estados Unidos. This Binational Centre had as its mission promoting understanding between the American and Brazilian people through cultural and educational activities and could award Fulbright scholarships. Palis applied and, after being examined by a committee, was awarded a Fulbright scholarship. The committee said that they would choose the best place in the United States for him to study but Palis told them that he would only accept if he could go to Columbia University and study under Smale.

In June 1964 Smale wrote to Palis saying that he was accepting a position at the University of California at Berkeley. Since it was too late for Palis to apply to study at Berkeley he wrote to Smale asking what he should do. He was told not to worry, that Smale would speedily arrange his enrolment. At Berkeley, Palis studied at first for a Master's Degree which he was awarded in 1966. He was undertaking research for his doctorate while studying for the Master's Degree and was able complete work on his thesis On Morse-Smale Diffeomorphisms by September 1967. He submitted a paper with the same title as his thesis to the American Mathematical Society in February 1968. It has the following note:-
The results announced here are contained in the author's doctoral thesis at the University of California, written while he held a fellowship from C.N. Pq., Brazil. The author wishes to thank Professor S Smale for his guidance.
In his thesis he proved that, in dimension no greater that 3, the set of Morse-Smale diffeomorphisms is open and its elements are structurally stable. Palis was awarded a Ph.D. for his thesis in 1968 and had two further papers published in that year: On Morse-Smale dynamical systems; and On the local structure of hyperbolic points in Banach spaces.

After completing work of his thesis, Palis visited Brown University in late 1967. Alberto Verjovsky writes [39]:-
I remember vividly when I saw Jacob Palis for the first time at Brown University in the winter of 1967. He was there to visit my advisor Maurício Peixoto and gave a beautiful seminar about his thesis at Berkeley under Stephen Smale. I was immediately impressed by his mathematics but also by his kindness and generosity in sharing ideas.
Palis also visited the Massachusetts Institute of Technology and Harvard. He returned to Berkeley in February 1968 where he had been offered a position as Assistant Professor. The fifteenth Summer Mathematical Institute of the American Mathematical Society, with the topic of global analysis was to be held at Berkeley from 1 July to 26 July and Palis was keen to attend. Palis has two papers in the Proceedings of the Symposium, namely A note on Ω\Omega-stability and (with Stephen Smale) Structural stability theorems. Kenneth Meyer reviews the second of these papers in [29] and writes:-
This paper proves that the class of diffeomorphisms or vector fields called Morse-Smale systems are structurally stable on an arbitrary compact n-manifold. This settles an old conjecture about structurally stable systems and generalises a result of M M Peixoto for 2-manifolds and the result of the first author for 3-manifolds in "On Morse-Smale diffeomorphisms'', Ph.D. Thesis, University of California, Berkeley, California, 1968.
In August 1968 Palis returned to Brazil and he explained his reasons in the interview [26]:-
At that time, Elon Lima, who had been a professor in Brasilia and then had come back to IMPA, was at Berkeley as a visiting professor. Manfredo do Carmo, another colleague and mathematician, was there as well, studying for his post-doctorate degree. I used to talk to them a lot and we had the impression that Brazil had very few mathematicians - but those few were top notch, especially Leopoldo Nachbin and Maurício Peixoto. These two professors spent long period abroad for scientific and other reasons. Elon, Manfredo and I had the feeling that it would be important to have a permanent scientific environment, where research studies would be conducted systematically and new researchers would also be systematically trained.
Back in Rio de Janeiro, Palis accepted posts at both the Federal University of Rio de Janeiro and at the Institute of Pure and Applied Mathematics. In the summer of 1969 he spent some time at the Differential Equations Symposium at the University of Warwick and both Palis and Smale are in June 1969 Conference photograph.

During this visit to Europe, he also visited the Institut des Hautes Études Scientifiques in France where the American mathematician Harold William Rosenberg (born 1941) was working. In 1970 Palis was elected to the Brazilian Academy of Sciences. In that year, he decided that he did not want to divide his work between two institutions and from that time on worked only at the IMPA.

In 1970, Elon Lima, Maurício Peixoto and Palis were organising the first International Symposium on Dynamical Systems, to be held at the University of Bahia, Salvador, Brazil from 26 July to 14 August 1971. This became possible through a chance meeting of Palis and José Pelúcio Ferreira one day when Palis got off at a different bus stop from his usual one and took a longer walk home. Pelúcio was Deputy Secretary General of the Ministry of Planning and General Coordination and managed the newly created National Fund for Scientific and Technological Development. Palis spoke with great enthusiasm to him about a new doctoral programme they were introducing at IMPA and said that it would be good for their students if they could organise an international conference. Pelúcio promised funding while the two men chatted on a quiet little street. In [28] Palis explains why the conference was held at the University of Bahia:-
... our conditions, on Rua Luís de Camões, at that point, really did not allow us to hold a large meeting. Five years later this was possible due to modifications that were made, but at that time the building, which is very beautiful, was not suitable for a mathematics institute. So the three committee members, we decided on something different. Why not think of a centre, for example, in the northeast? ... The idea was to open up a little space for mathematical activity in the country. Also, on the other hand, given that the meeting would be attended by many mathematicians and students, especially from Rio and, in part, from São Paulo, we thought that the location itself was not very important, as long as it was suitable for the meeting. ... We then left for a visit to Salvador, Recife and Fortaleza. In fact Salvador, due to the fact that it was opening a new building for Mathematics, naturally imposed itself.
The new doctoral programme at IMPA began with great success with three of Palis's students completing their degree by 1973: Welington de Melo (Structural Stability on 2-Dimension Manifolds), Pedro Mendes (Estabilidade em Variedades Abertas ) and Ricardo Mañé (Persistent Invariant Manifolds are Normally Hyperbolic). In 1972 Palis was awarded a John Simon Guggenheim Fellowship which enabled him to spend 1973 at the University of California at Berkeley.

Palis was awarded the Moinho Santista Prize in 1976; this is the most prestigious prize for science in Brazil. He was an invited speaker at the International Congress of Mathematicians in Helsinki in 1978 giving the address Moduli of stability and bifurcation theory. He dedicated his talk "To Rufus Bowen, in memoriam." The talk begins:-
Bifurcation theory of dynamical systems goes as far back as Poincaré. One aims at describing the changes in the phase portrait (space of orbits) of a system depending on parameters when such parameters vary. This lecture concerns a line of recent developments in this direction, especially on bifurcations of one parameter families of vector fields and diffeomorphisms. A relevant role, in this context, is played by certain differentiable invariants of topological equivalence for systems that exhibit non-transversal saddle connections. Such invariants bring up, in a natural way, the notion of moduli of stability in dynamical systems. They also imply, as explained in one of the topics below, the existence of moduli of stability for holomorphic vector fields near a singularity.
As he did in 1969, Palis went to Europe in the summer of 1980 and again spent a little time at both the University of Warwick in England and at the Institut des Hautes Études Scientifiques in France. This began a series of regular visits, roughly every two years, usually to Europe but in 1984 to the United States and in 1988 to Japan. Also in 1988, along with Chris Zeeman, he organised the four-week long Summer School on Dynamical Systems held in Trieste, Italy. Palis taught the course "Introduction to Dynamical Systems: Geometric Theory" with problem sessions run by Rodrigo Bamon and Maria Josè Pacifico.

Giving details of the extraordinary research contributions that Palis has made requires deep technical details; these are given in [30]. Our best option is to let Palis himself describe his contributions, quoting from the acceptance speech he gave in Italy when receiving the Balzan Prize in 2010 [13]:-
In the development of my scientific work, I have travelled a long way, from the global stability of dynamical systems, to the bifurcations of Poincaré's cycles and fractal dimensions and finally, to a meaningful proposal of a global scenario for dynamics, comprising chaotic systems. I have begun to prove that gradient-like dynamical systems in lower dimensions are stable, meaning that the structure of their orbit remains qualitatively the same under small perturbations of the law of evolution. This has considerably extended a previous remarkable work by Peixoto. The methods of proof used, have embodied a new geometric approach that will fundamentally influence subsequent developments in this area of research: the creation of the notion of stable foliations being partially subfoliated to include those of critical points or isolated period motions of higher indices where they accumulate. Immediately after that, this result was extended to all dimensions in a joint work with Smale, who had been my thesis adviser. Together, we formulated the well-known stability conjecture that became a major topic of research in the area, partially solved, about two decades later, in a remarkable exposition by Mañé, one of my students, and subsequently by Hyashi in a similar context. Liao also contributed to the solution of this question. Since the early seventies, I have become very interested in the theory of bifurcations of Poincaré's cycles, together with Newhouse and, sometime later, Takens. It became clear that fractal dimensions would play a key role in understanding such bifurcations. My early collaboration with Newhouse and Takens was later extended to Yoccoz and Viana in the eighties and then Moreira in the nineties. Together, we have proved that fractal dimensions indeed determine the frequency of stability in homoclinic bifurcations in all dimensions. The case of heterodimensional cycles in higher dimensions have been successfully considered by Bonatti, Diaz and Rocha, among others. Based on previous work, I was able to formulate by 1995 a bold series of ideas and conjectures that encompassed a global view of dynamics with much more of a probabilistic character than attempted before. The Russian school of Kolmogorov and Sinai, among others, was inspiring. Such a programme has spurred significant activity and some successful results derived from this can be seen in works by Lyubich, de Melo, Avila, Moreira, Martens, Viana, and also Abdenur, Bonatti, Diaz, Rocha, Crovisier, Pujals, Sambarino and Wen among others, as well as Yoccoz and myself.
For Palis's own description of the Balzan Project that he carried out 2011-2015 funded by the award of the Balzan Prize, see THIS LINK.

For information about books written by Palis, see THIS LINK.

In addition to the prizes we have mentions, Palis has also won The World Academy of Science Prize (1988), the National Prize for Science and Technology, Brazil (1990), the InterAmerican Prize for Science from the Organization of the American States (1995), the Prize Mexico for Science and Technology (2001), the Trieste Science Prize in Mathematics (2006), the Accademia Nazionale dei Lincei International Prize (2008), and the Abdus Salam Medal (2015).

There is another important contribution that Palis has made to mathematics, namely the leading roles he has played in both Brazilian and International Scientific Institutions. In Brazil he served as Director of the Instituto Nacional de Matemática Pura e Aplicada (IMPA) 1993-2003, and has been a member of the Scientific Committee of National Research Council of Brazil 1988-1992; 1994-1998; and 2001-2005. He served as a director of the Brazilian Academy of Sciences 1977-1979; 1979-1981; and 2001-2004. He was elected Vice-President of the Brazilian Academy of Sciences 1999-2001 and its President 2007-2010. On the international scene he served as a member of the Executive Board for the International Council for Science 1993-1996, and was its Vice-President 1996-1999. He was a member of Executive Board of the International Mathematical Union 1982-1991, its Secretary 1991-1999 and its President 1991-1999. He was a Founding Member of the Latin American and Caribbean Mathematical Union and served as the Chair of its first Scientific Committee. He was a member of the Scientific Advisory Committee of the Eidgenössische Technische Hochschule Zürich 1990-2006. He was Secretary General of the The World Academy of Sciences 2000-2006, then its President 2007-2010.

Let us end with a couple of quotes. First from Sheldon Newhouse [30]:-
I think it's really fair to say that in our time Jacob Palis has been one of the main figures responsible for the development of Mathematics and Science, primarily in Latin America and, in fact, in many other places, through his organisation of meetings, symposia, workshops, and the support of sciences and Mathematics in developing countries, most notably, that I'm familiar with, in Trieste. He has facilitated the contacts between scientists who have had great difficulty in traveling to the west for political or other reasons. They were able to establish contacts with western mathematicians in the settings of meetings, workshops, and schools where one can get to meet many people. I myself met a number of people from mainland China in Trieste, at a time when it was extremely difficult for them to travel to Western Europe. Jacob has been one of the primary organisers and supporters of such occasions. Moreover, he has been responsible, in great measure, for the tremendous growth of IMPA, this wonderful institute, as a researcher and, more recently, also as the Director. I think it's fair to say that IMPA has become the principal centre for Mathematics in Latin America and, certainly, one of the world centres for Dynamical Systems. In no small measure is this due to his efforts and, again, his vision.
Finally a quote from David Mumford, see page 28 of [1]:-
I have come to believe that something like 50% of research mathematicians are somewhere on the "autistic spectrum". How could it be otherwise? Research for most of us is a solitary occupation, necessitating endless hours of mulling over abstract ideas, trying to sort them out and imprint their key ideas into our brains. This can be torture for the gregarious nature. But now and then, someone comes along who transcends this trap, someone who can work collaboratively and also love the give and take of mathematical discussion. Even rarer is the individual who possesses such personal charisma that both powerful and wealthy people rise to the challenge of understanding the deep importance of mathematics - then, wonder of wonders, they agree to fully support our work. Needless to say, this great institute IMPA would never have existed without your stewardship, your infectious enthusiasm and the political skills that brought it into existence. The IMPA is something like Coleridge's Xanadu, a true pleasure dome for our community of mathematics lovers. There it is, rising above the chaotic craziness of Rio into the midst of a beautiful tropical forest, an assembly of intense people drinking the strongest Brazilian coffee and talking mathematics! ... What you have accomplished, that I have glimpsed from afar, is something so inspiring that it has often made me wish for a second life to devote to that field. One thing I do know: we had tremendous fun working together all over the world at meetings of the International Mathematical Union and I have had so much unforgettable pleasure and delight from my half dozen visits to Rio at your invitation.

References (show)

  1. Conference Jacob Palis at IMPA: On the occasion of his 80th birthday, Instituto de Matemática Pura e Aplicada, Rio de Janeiro (2020).
  2. I F Corbett (ed.), Proceedings of the Twenty Seventh General Assembly Rio de Janeiro 2009. Transactions of the International Astronomical Union XXVIIB (Cambridge University Press, 2010).
  3. L J Díaz, Review: Jacob Palis - Selected Works, by Welington de Melo (ed.), Mathematical Reviews MR3287578.
  4. L J Díaz, F Lenarduzzi, S Lima and M J Pacifico (eds.), His 80th birthday. Jacob Palis: man, scientist, friend (Instituto de Matemática Pura e Aplicada, Rio de Janeiro, March 2020).
  5. A Dimca, Review: Geometry and Topology, by J Palis and M do Carmo, Bulletin mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie 26 (74) (4) (1982), 392.
  6. A Georgescu, Review: Geometric theory of dynamical systems, An Introduction, by J Palis and W De Melo, Bulletin mathématique de la Société des Sciences Mathématiques de la RépubliqueSocialiste de Roumanie 32 (80) (1) (1988), 92.
  7. M Hurley, Review: Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, by Jacob Palis Jr and Floris Takens, Mathematical Reviews MR1237641 (94h:58129).
  8. IMU Executive Committees 1952-2014, International Mathematical Union (8 January 2015).
  9. Jacob Palis. Presidente da Academia Brasileira de Ciências, Academia Brasileira de Ciências.
  10. Jacob Palis, List of Members, Deutsche Akademie der Naturforscher Leopoldina.
  11. Jacob Palis, Interview with Jacob Palis and Welington De Melo, 2010 Balzan Prize for Mathematics (Pure and Applied) (15 December 2014).
  12. Jacob Palis, Bio-bibliography, 2010 Balzan Prize for Mathematics (Pure and Applied) (October 2010).
  13. Jacob Palis, Acceptance Speech - Rome 19.11.2010, 2010 Balzan Prize for Mathematics (Pure and Applied) (19 November 2010).
  14. Jacob Palis, Dynamical Systems. Chaotic Behaviour - Uncertainty, 2010 Balzan Prize for Mathematics (Pure and Applied) (18 November 2010).
  15. Jacob Palis, The Balzan Prizewinners' Research Projects: An Overview 2020, 2010 Balzan Prize for Mathematics (Pure and Applied) (2020).
  16. Jacob Palis, The International Who's Who 2013, 76th Edition (Routledge, New York, 2012.
  17. Jacob Palis, Who's Who in the World, 22nd Edition (Marquis Who's Who, New Providence, New York, 2006).
  18. Jacob Palis, Who's Who in the World, 29th Edition (Marquis Who's Who, New Providence, New York, 2012).
  19. Jacob Palis, Who's Who in Science and Engineering. 7th edition, 2004-2005 (Marquis Who's Who, New Providence, New York, 2003).
  20. Jacob Palis, International Mathematical Union (1995).
  21. Jacob Palis Jr., President, Biography, InterAcademyPartnership.
  22. Jacob Palis Jr., National Academy of Sciences (2022).
  23. Jacob Palis Jr., Fellows, John Simon Guggenheim Foundation (2022).
  24. R L Kraft, Review: Hyperbolicity & Sensitive Chaotic Dynamics at Homoclinic Bifurcations, by J Palis and F Takens, SIAM Review 38 (2) (1996), 348-349.
  25. S Marmi, How I met Jacob Palis and how he changed my life, Instituto de Matemática Pura e Aplicada, Rio de Janeiro (March 2020).
  26. F Marques, Jacob Palis Júnior: Healthy uncertainty, Pesquisa 161 (July 2009).
  27. W de Melo (ed.), Jacob Palis - Selected Works (Springer 2014).
  28. P Mendes, E L Lima, J Palis and M Viana, Homenagem A Ricardo Mañé, Matemática Universitária 18 (1995), 1-18.
  29. K R Meyer, Review: Structural stability theorems, by J Palis and S Smale, Mathematical Reviews MR0267603 (42 #2505).
  30. S Newhouse, On the mathematical contributions of Jacob Palis, Astérisque 286 (2003), 1-24.
  31. Palis Awarded Balzan Prize, Notices of the American Mathematical Society 58 (1) (2011), 66-67.
  32. Palis Elected TWAS President, Third World Academy of Sciences (15 July 2007).
  33. J Palis and F Lenarduzzi, Welington de Melo and Jacob Palis: their first meeting, some of their work on structural stability and a lifetime of friendship, in New trends in one-dimensional dynamics (Springer, 2019), 1-5.
  34. J Palis, Fulfilling the promise, in Daniel Schaffer (ed.), Twas:
  35. J Palis, Interview: Science for Development, TWAS Newsletter (2007), 34-39.
  36. J Palis, An Academy of sciences for the Developing world, A World of Science 6 (1) (2008), 14-15.
  37. J Robbin, Review: Geometric Theory of Dynamical Systems: An Introduction, by Jacob Palis and Welington de Melo, The American Mathematical Monthly 91 (7) (1984), 448-449.
  38. University of Warwick honorary degrees 2000, Warwick News and Events, University of Warwick (10 April 2000).
  39. A Verjovsky, Some remembrances of Jacob Palis, Instituto de Matemática Pura e Aplicada, Rio de Janeiro (March 2020).
  40. R B Walker, Review: Geometric theory of dynamical systems, by Jacob Palis Jr and Welington de Melo, Mathematical Reviews MR0669541 (84a:58004).
  41. S van Strien, Review: Homoclinic bifurcations and hyperbolic dynamics, by Jacob Palis Jr and Floris Takens, Mathematical Reviews MR0953789 (90a:58143).

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Written by J J O'Connor and E F Robertson
Last Update February 2023