Jacob Palis - Selected Works

ISBN-13: 9783319069678 / Angielski / Twarda / 2014 / 711 str.

Jacob Palis; Jacob Palis Junior; Welington De Melo

Opis

The Theory of Dynamical Systems was first introduced by the great mathematician Henri Poincare as a qualitative study of differential equations. For more than forty years, Jacob Palis has made outstanding contributions to this area of mathematics. In the 1970s, following in the wake of Stephen Smale, he became one of the major figures in developing the Theory of Hyperbolic Dynamics and Structural Stability.This volume presents a selection of Jacob Palis' mathematical contributions, starting with his PhD thesis and ending with papers on what is widely known as the Palis Conjecture. Most of the papers included in the present volume are inspired by the earlier work of Poincare and, more recently, by Steve Smale among others. They aim at providing a description of the general structure of dynamical systems.Jacob Palis, whose work has been distinguished with numerous international prizes, is broadly recognized as the father of the Latin American School of Mathematics in Dynamical Systems and one of the most important scientific personalities on the continent. In 2010 he was awarded the Balzan Prize for his fundamental contributions in the Mathematical Theory of Dynamical Systems, which has been the basis for many applications in various scientific disciplines.

Spis treści

A Short Summary of my Scientific Life: J. Palis.- On Morse-Smale Dynamical Systems:  J. Palis.- Structural Stability Theorems: J. Palis and S. Smale.- A Note on Ω-Stability: J. Palis.- Neighborhoods of Hyperbolic Sets: M. Hirsch, J. Palis, C. Pugh and M. Shub.- Hyperbolic Non wandering Sets on Two-Dimensional Manifolds: S. Newhouse and J. Palis.- The Topology of Holomorphic Flows with Singularity: C. Camacho, N.H. Kuiper and J. Palis.- Topological Equivalence of Normally Hyperbolic Dynamical Systems: J. Palis and F. Takens.- Moduli of Stability and Bifurcation Theory: J. Palis.- Characterising Diffeomorphisms with Modulus of Stability One: W. de Melo, J. Palis and S.J. van Strien.- Bifurcations and Stability of Families of Diffeomorphisms: S. Newhouse, J. Palis and F. Takens.- Stability of Parametrized Families of Gradient Vector Fields: J. Palis and F. Takens.- A Note on the Inclination Lemma (λ-Lemma) and Feigenbaum's Rate of Approach: J. Palis.- Cycles and Measure of Bifurcation Sets for Two-Dimensional Diffeomorphisms: J. Palis and F. Takens.- Hyperbolicity and the Creation of Homoclinic Orbits:J. Palis and F. Takens.- On the C1 Ω-Stability Conjecture: J. Palis.- Centralizers of Anosov Diffeomorphisms on Tori: J. Palis and J.- C. Yoccoz.- Homoclinic Tangencies for Hyperbolic Sets of Large Hausdorff Dimension: J. Palis and J.- C. Yoccoz.- High Dimension Diffeomorphisms Displaying Infinitely Many Periodic Attractors: J. Palis and M. Viana.- On the Arithmetic Sum of Regular Cantor Sets: J. Palis and J.-C. Yoccoz.- A Global View of Dynamics and a Conjecture on the Denseness of Finitude of Attractors: J. Palis.- Fers à cheval non uniformément hyperboliques engendrés par une bifurcation homocline et densité nulle des attracteurs. (French) [Non-Uniformly Hyperbolic Horseshoes Generated by Homoclinic Bifurcations and Zero Density of Attractors]: J. Palis and J.-C. Yoccoz.- Homoclinic Tangencies and Fractal Invariants in Arbitrary Dimension: C.G. Moreira, J. Palis and M. Viana.- A Global Perspective for Non-Conservative Dynamics: J. Palis.- Non-Uniformly Hyperbolic Horseshoes Arising From Bifurcations of Poincaré Heteroclinic Cycles: J. Palis and J.- C. Yoccoz.- List of Publications of Jacob Palis Junior.- List of Ph.D. Students of Jacob Palis Junior at IMPA.- Acknowledgements.

O autorze

Jacob Palis is a member of the Brazilian Academy of Science and a professor at IMPA, Rio de Janeiro. He has received many international prizes, he is a member of thirteen Academies of Sciences and a holder of honorary degrees from six universities. In 2010 he was awarded the Balzan Prize for his fundamental contributions in the Mathematical Theory of Dynamical Systems.