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Differential Equations, Dynamical Systems, and an Introduction to Chaos

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Author(s): Morris W. Hirsch, Stephen Smale and Robert L. Devaney (Auth.)
Publisher: Academic Press
Year: 2012

Language: English
Pages: 416
Tags: Математика;Дифференциальные уравнения;

Content:
Front Matter, Page i
Copyright, Page ii
Preface to Third Edition, Page ix
Preface, Pages xi-xiv
1 - First-Order Equations, Pages 1-19
2 - Planar Linear Systems, Pages 21-38
3 - Phase Portraits for Planar Systems, Pages 39-59
4 - Classification of Planar Systems, Pages 61-72
5 - Higher-Dimensional Linear Algebra, Pages 73-105
6 - Higher-Dimensional Linear Systems, Pages 107-138
7 - Nonlinear Systems, Pages 139-157
8 - Equilibria in Nonlinear Systems, Pages 159-186
9 - Global Nonlinear Techniques, Pages 187-212
10 - Closed Orbits and Limit Sets, Pages 213-232
11 - Applications in Biology, Pages 233-255
12 - Applications in Circuit Theory, Pages 257-276
13 - Applications in Mechanics, Pages 277-303
14 - The Lorenz System, Pages 305-328
15 - Discrete Dynamical Systems, Pages 329-359
16 - Homoclinic Phenomena, Pages 361-384
17 - Existence and Uniqueness Revisited, Pages 385-409
Bibliography, Pages 411-413
Index, Pages 415-418