[PDF] [1982] Geometric Theory of Dynamical Systems An Introducti

DOWNLOAD MORE EBOOKS, MAGAZINES, & PDFS: http://buyabook.ws/download-ebooks-magazines-pdfs-more/ BOOK INFO: Geometric Theory of Dynamical Systems: An Introduction By J. Jr. Palis, W. de Melo Publisher: Springer Number Of Pages: 198 Publication Date: 1982-08-18 ISBN-10 / ASIN: 0387906681 ISBN-13 / EAN: 9780387906683 This book grew from courses and seminars taught at IMPA and several other institutions both in Brazil and abroad, a first text being prepared for the Xth Brazilian Mathematical Colloquium. With several additions, it later became a book in the Brazilian mathematical collection Projeto Euclides, published in Portuguese. A number of improvements were again made for the present translation. We are most grateful to many colleagues and students who provided us with useful suggestions and, above all, encouragement for us to present these introductory ideas on Geometric Dynamics. We are particularly thankful to Paulo Sad and, especially to Alcides Lins Neto, for writing part of a first set of notes, and to Anthony Manning for the translation into English. Contents List of Symbols Chapter 1 Differentiable Manifolds and Vector Fields 1 1 Calculus in 6d" and Differentiable Manifolds 1 2 Vector Fields on Manifolds 10 3 The Topology of the Space of C'^\infty Maps 19 4 Transversality 23 5 Structural Stability 26 Chapter 2 Local Stability 39 1 The Tubular Flow Theorem 39 2 Linear Vector Fields 41 3 Singularities and Hyperbolic Fixed Points 54 4 Local Stability 59 5 Local Classification 68 6 Invariant Manifolds - 73 7 The A-lemma (inclination Lemma). Geometrical Proof of Local Stability 80 Chapter 3 The Kupka-Smale Theorem 91 1 The Poincare Map 92 2 Genericity of Vector Fields Whose Closed Orbits Are Hyperbolic 99 3 Transversality of the Invariant Manifolds 106 Chapter 4 Genericity and Stability of Morse-Smale Vector Fields 115 1 Morse-Smale Vector Fields; Structural Stability 116 2 Density of Morse-Smale Vector Fields on Orientable Surfaces 132 3 Generalizations 150 4 General Comments on Structural Stability. Other Topics 153 Appendix: Rotation Number and Cherry Flows 181 References 189 Index 195

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