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Jacob PalisJacob Palis, Jr. (b. 1940 in Uberaba, Brazil) is one of the few Brazilian mathematicians of international recognition. Since 1973 he has held a permanent position as professor at Instituto Nacional de Matemtica Pura e Aplicada in Rio de Janeiro, Brazil. He was director of the same institute from 1993 until 2003. 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. Research interests Mainly dynamical systems and differential equations. Some themes are: Global stability and hyperbolicity, bifurcations, attractors and chaotic systems. 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. Astrisque. Frana: , 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.
External links Palis, Jacob Palis, Jacob
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