Jacob Palis

From Wikipedia, the free encyclopedia

Jacob Palis, Jr. (b. 15 March 1940 in Uberaba, Brazil) is a Brazilian mathematician of international recognition. Since 1973 he has held a permanent position as professor at 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 [1].

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.

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.

His Erdös number is 3.

Contents 1 Research interests 2 Selected publications 3 Books published 4 External links

[edit] Research interests

Mainly dynamical systems and differential equations. Some themes are: Global stability and hyperbolicity, bifurcations, attractors and chaotic systems.

[edit] Selected publications

1. On Morse-Smale Dynamical Systems, Topology 19, 1969 (385-405).
2. Structural Stability Theorems, with S. Smale, Proceedings of the Institute on Global Analysis, American Math. Society, Vol. XIV, 1970 (223-232).
3. Cycles and Bifurcations Theory, with S. Newhouse, Asterisque 31, Societe Mathematique de France, 1976 (44-140).
4. The Topology of Holomorphic Flows near a Singularity, with C. Camacho and N. Kuiper, Publications Math.Institut Hautes Etudes Scientifiques 48, 1978 (5-38).
5. Moduli of Stability and Bifurcation Theory, Proceedings of the International Congress of Mathematicians, Helsinki, 1978 (835-839).
6. Stability of Parameterized Families of Gradient Vector Fields, with F. Takens, Annals of Mathematics 118, 1983 (383-421).
7. Cycles and Measure of Bifurcation Sets for Two-Dimensional Diffeomorphisms, with F. Takens, Inventiones Mathematicae 82, 1985 (397-422).
8. Homoclinic Orbits, Hyperbolic Dynamic and Fractional Dimensions of Cantor Sets (Lefschetz Centennial Conference) Contemporary Mathematics - American Mathematical Society, 58, 1987 (203-216).
9. Hyperbolicity and Creation of Homoclinic Orbits, with F.Takens, Annals of Mathematics 125, 1987 (337-374).
10. On the C1 Omega-Stability Conjecture, Publications Math. Institut Hautes Etudes Scientifiques, 66, 1988 (210-215).
11. 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).
12. Homoclinic Tangencies for Hyperbolic Sets of Large Hausdorff Dimension, with J.C. Yoccoz, Acta Mathematica 172, 1994 (91-136).
13. High Dimension Diffeomorphisms Displaying Infinitely Many Sinks, with M. Viana, Annals of Mathematics 140, 1994 (207 - 250).
14. A Global View of Dynamics and a Conjecture on the Denseness of Finitude of Attractors. Astérisque. França: , v.261, p.339 - 351, 2000.
15. Homoclinic tangencies and fractal invariants in arbitrary dimension, with C. Moreira and M. Viana, C R Ac Sc Paris., 2001.
16. Nonuniformily hyperbolic horseshoes unleashed by homoclinic bifurcations and zero density of attractors, with J.-C. Yoccoz, C R Ac Sc Paris., 2001.

[edit] Books published

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

[edit] External links

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