Jacob Palis

Jacob Palis, Jr. ( born March 15, 1940 in Uberaba, Minas Gerais ) is a Brazilian mathematician and university professor.

Biography

After school he studied at the University of California, Berkeley in 1968 and earned a Philosophiae Doctor ( Ph.D.) in Stephen Smale with a dissertation on the topic On Morse - Smale diffeomorphisms. After his return to Brazil he was in 1973 professor at the National Institute of Pure and Applied Mathematics ( Instituto Nacional de Matemática Pura e Aplicada ) in Rio de Janeiro as its director from 1993 to 2003. As a high school teacher, he was next to doctoral supervisor of more than forty students. As a scientist, he was primarily concerned with questions of dynamical systems, differential equations, metastability, bifurcation, attractors and chaos research.

Between 1999 and 2002 he was also President of the International Mathematical Union. After 2004 he was first secretary general, and finally in 2006 president of the Academy of Sciences for the Developing World, the former Third World Academy of Sciences ( TWAS ).

For his scientific achievements he has won several awards and is not only a member of the National Academy of Sciences, the Academy of Sciences and the Leopoldina, but since 2005, Knight of the Legion of Honour. In addition, he received the price of the Universities of Brazil (1962), Moinho Santista (1976 ), the TWAS (1994) and the Inter-American Science Prize (1994 ). In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki ( moduli of stability and bifurcation theory ).

In September 2010, Palis was "for his fundamental contributions to the mathematical theory of dynamical systems " was awarded the Balzan Prize. In the award statement also stated that " he has delivered significant contributions to the theory of differential equations and dynamical systems in the course of his career, which were the basis for numerous applications in a wide variety of scientific disciplines. Since the study of chemical oscillators and Paul Schuster's analysis of models of prebiotic evolution, the theory of dynamical systems is also applied in chemistry. "

His doctoral include Welington de Melo, Marcelo Viana, Ricardo Enrique Pujals and Mañé.

Publications

Palis, whose Erdős number "3" is published in the course of his scientific career numerous technical papers and reference books.

Essays

• On Morse - Smale Dynamical Systems, Topology 19, 1969 ( 385-405 ).
• With Stephen Smale Structural Stability theorem, Proceedings of the Institute on Global Analysis, American Mathematical Society, Vol XIV, 1970 ( 223-232 ).
• With Sheldon Newhouse Cycles and Bifurcations Theory, astérisque 31, Mathematique Societe de France, 1976, 44-140.
• With C. Camacho, Nicolaas Kuiper: The Topology of holomorphic flows near a Singularity, 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 ).
• Floris Takens with Stability of Parameterized Families of Gradient Vector Fields, Annals of Mathematics 118, 1983 ( 383-421 ).
• With Takens Cycles and measure of bifurcation sets for Two -Dimensional diffeomorphisms, Inventiones Mathematicae 82, 1985 ( 397-422 ).
• Homo Clinic orbits, Hyperbolic Dynamic and Fractional Dimensions of Cantor sets ( Lefschetz Centennial Conference) Contemporary Mathematics - American Mathematical Society, 58, 1987 ( 203-216 ).
• With Takens Hyperbolicity and Creation of homo clinic orbits, Annals of Mathematics 125, 1987 ( 337-374 ).
• On the C1 Omega Stability Conjecture, Publications Math Institute Hautes Etudes Scientifiques, 66, 1988 ( 210-215 ).
• With MJ Carneiro Bifurcations and Global Stability of Two - Parameter Families of Gradient Vector Fields, Publications Math Institute Hautes Etudes Scientifiques 70, 1990 ( 103-168 ).
• With Jean-Christophe Yoccoz Homo Clinic Tangencies for Hyperbolic Sets of Large Hausdorff dimension, Acta Mathematica 172, 1994, 91-136
• With Marcelo Viana High dimension diffeomorphisms Displaying Infinitely Many Sinks, Annals of Mathematics 140, 1994, 207-250
• A Global View of Dynamics and a Conjecture on the denseness of Finitude of Attractors, astérisque. França: , Volume 261, 2000, pp. 339-351
• With C. Moreira, M. Viana homo clinic tangencies and fractal invariants in arbitrary dimension, CR Ac Sc Paris., 2001.
• With Yoccoz Nonuniformily hyperbolic horseshoes unleashed by homo clinic Bifurcations and zero density of attractors, CR Ac Sc Paris., 2001.

Reference Books

• With W. de Melo, Geometric Theory of Dynamical Systems, Springer-Verlag, 1982.
• With Takens Hyperbolicity and Sensitive Chaotic Dynamics at Homo Clinic Bifurcations, Fractal Dimensions and Infinitely Many Attractors, Cambridge University Press, 1993; Second edition, 1994.