Differential Equations, Dynamical Systems, and an Introduction to ChaosAcademic Press, 2004 - 417 páginas Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition, provides a rigorous yet accessible introduction to differential equations and dynamical systems. The original text by three of the world's leading mathematicians has become the standard textbook for graduate courses in this area. Thirty years in the making, this Second Edition brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The book explores the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It presents the simplification of many theorem hypotheses and includes bifurcation theory throughout. It contains many new figures and illustrations; a simplified treatment of linear algebra; detailed discussions of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor; and increased coverage of discrete dynamical systems. This book will be particularly useful to advanced students and practitioners in higher mathematics.
NEW IN THIS EDITION
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Conteúdo
Chapter 1 FirstOrder Equations | 1 |
Chapter 2 Planar Linear Systems | 21 |
Chapter 3 Phase Portraits for Planar Systems | 39 |
Chapter 4 Classification of Planar Systems | 61 |
Chapter 5 Higher Dimensional Linear Algebra | 75 |
Chapter 6 Higher Dimensional Linear Systems | 107 |
Chapter 7 Nonlinear Systems | 139 |
Chapter 8 Equilibria in Nonlinear Systems | 159 |
Chapter 11 Applications in Biology | 235 |
Chapter 12 Applications in Circuit Theory | 257 |
Chapter 13 Applications in Mechanics | 277 |
Chapter 14 The Lorenz System | 303 |
Chapter 15 Discrete Dynamical Systems | 327 |
Chapter 16 Homoclinic Phenomena | 359 |
Chapter 17 Existence and Uniqueness Revisited | 383 |
Bibliography | 407 |
Chapter 9 Global Nonlinear Techniques | 189 |
Chapter 10 Closed Orbits and Limit Sets | 215 |
Outras edições - Ver todos
Differential Equations, Dynamical Systems, and an Introduction to Chaos Stephen Smale,Morris W. Hirsch,Robert L. Devaney Prévia não disponível - 2003 |
Differential Equations, Dynamical Systems, and an Introduction to Chaos Morris W. Hirsch,Stephen Smale,Robert L. Devaney Prévia não disponível - 2003 |
Termos e frases comuns
Referências a este livro
An Introduction to Infinite-Dimensional Linear Systems Theory Ruth F. Curtain,Hans Zwart Visualização parcial - 1995 |
Manifolds, Tensor Analysis, and Applications Ralph Abraham,J.E. Marsden,Tudor Ratiu Visualização parcial - 1993 |