Jacob Palis

Jacob Palis
Born	(1940-03-15) 15 March 1940 Uberaba, Brazil
Nationality	Brazilian
Fields	Mathematics
Institutions	Instituto Nacional de Matemática Pura e Aplicada
Alma mater	University of California, Berkeley Federal University of Rio de Janeiro
Doctoral advisor	Stephen Smale
Doctoral students	Welington de Melo Ricardo Mañé Marcelo Viana Enrique Pujals
Notable awards	Balzan Prize (2010) Abdus Salam Medal (2015)

Jacob Palis, Jr. (born 15 March 1940) is a Brazilian mathematician and professor. Palis' research interests are mainly dynamical systems and differential equations. Some themes are: Global stability and hyperbolicity, bifurcations, attractors and chaotic systems.

Biography

Jacob Palis was born in Uberaba, Minas Gerais. His father was a Lebanese immigrant, and his mother was a Syrian immigrant. The couple had eight children (five men and three women), and Jacob was the youngest. His father was a merchant, owner of a large store, and supported and funded the studies of his children. Palis said that he already enjoyed mathematics in his childhood.^[1][2]

At 16, Palis moved to Rio de Janeiro to study engineering at the University of Brazil – now UFRJ – (he was approved in first place in the entrance exam but was not old enough to be accepted, so he then had to take the university's entry exams again a year later, so he did, and obtained first place again). He completed the course in 1962 with honours and receiving the award for the best student.^[2]

In 1964, he moved to the United States. In 1966 he obtained his master's degree in mathematics under the guidance of Stephen Smale, and in 1968 his Ph.D., again with Smale as advisor.^[3][4]

In 1968, he returned to Brazil and became a researcher at the IMPA.^[3]

Since 1973 he has held a permanent position as professor at the Instituto Nacional de Matemática Pura e Aplicada in Rio de Janeiro, Brazil. He was director of the same institute from 1993 until 2003. He was Secretary-General of the Third World Academy of Sciences from 2004 to 2006, and elected its President in 2006^[5] and remained on position till December 2012. He was also president of the International Mathematical Union from 1999 to 2002.^[6] He is the current president of Brazilian Academy of Sciences since 2007.^[7]

He studied under Stephen Smale at University of California, Berkeley, and his 1968 thesis was entitled On Morse-Smale Diffeomorphisms. Palis himself has advised more than forty Ph.D. students so far from more than ten countries.

Awards and honours

Palis has received numerous medals and decoration. He is a foreign member of several academies of sciences, including the United States National Academy of Sciences and the French Academy of Sciences. In 2005 Palis was selected a member of the Legion of Honor.

He is a member of the Norwegian Academy of Science and Letters.^[8] In 2010 he was awarded the Balzan Prize for his fundamental contributions in the mathematical theory of dynamical systems that has been the basis for many applications in various scientific disciplines (such as in the study of oscillations).^[9]

His Erdős number is 3.

Palis serves on the board of the Science Initiative Group.

Selected publications

• On Morse-Smale Dynamical Systems, Topology 19, 1969 (385-405).
• Structural Stability Theorems, with S. Smale, Proceedings of the Institute on Global Analysis, American Math. Society, Vol. XIV, 1970 (223-232).
• Cycles and Bifurcations Theory, with S. Newhouse, Asterisque 31, Societe Mathematique de France, 1976 (44-140).
• The Topology of Holomorphic Flows near a Singularity, with C. Camacho and N. Kuiper, Publications Math.Institut Hautes Etudes Scientifiques 48, 1978 (5-38).
• Moduli of Stability and Bifurcation Theory, Proceedings of the International Congress of Mathematicians, Helsinki, 1978 (835-839).
• Stability of Parameterized Families of Gradient Vector Fields, with F. Takens, Annals of Mathematics 118, 1983 (383-421).
• Cycles and Measure of Bifurcation Sets for Two-Dimensional Diffeomorphisms, with F. Takens, Inventiones Mathematicae 82, 1985 (397-422).
• Homoclinic Orbits, Hyperbolic Dynamic and Fractional Dimensions of Cantor Sets (Lefschetz Centennial Conference) Contemporary Mathematics - American Mathematical Society, 58, 1987 (203-216).
• Hyperbolicity and Creation of Homoclinic Orbits, with F.Takens, Annals of Mathematics 125, 1987 (337-374).
• On the C1 Omega-Stability Conjecture, Publications Math. Institut Hautes Etudes Scientifiques, 66, 1988 (210-215).
• Bifurcations and Global Stability of Two-Parameter Families of Gradient Vector Fields with M. J. Carneiro, Publications Math. Institut Hautes Etudes Scientifiques 70, 1990 (103-168).
• Homoclinic Tangencies for Hyperbolic Sets of Large Hausdorff Dimension, with J.C. Yoccoz, Acta Mathematica 172, 1994 (91-136).
• High Dimension Diffeomorphisms Displaying Infinitely Many Sinks, with M. Viana, Annals of Mathematics 140, 1994 (207 - 250).
• A Global View of Dynamics and a Conjecture on the Denseness of Finitude of Attractors. Astérisque. França: , v.261, p.339 - 351, 2000.
• Homoclinic tangencies and fractal invariants in arbitrary dimension, with C. Moreira and M. Viana, C R Ac Sc Paris., 2001.
• Nonuniformily hyperbolic horseshoes unleashed by homoclinic bifurcations and zero density of attractors, with J.-C. Yoccoz, C R Ac Sc Paris., 2001.

Books published

• Geometric Theory of Dynamical Systems, with W. de Melo. Springer-Verlag, 1982; also published in Portuguese, Russian and Chinese.
• Hyperbolicity and Sensitive-Chaotic Dynamics at Homoclinic Bifurcations, Fractal Dimensions and Infinitely Many Attractors, with F. Takens. Cambridge Univ. Press, 1993; Second Edition, 1994.

References

External links

• Jacob Palis' homepage
• Jacob Palis at the Mathematics Genealogy Project