Introduction to applied nonlinear dynamical systems and chaos /
Wiggins, Stephen
Introduction to applied nonlinear dynamical systems and chaos / Stephen Wiggins. - Second edition - xix, 843 pages : illustrations ; 25 cm. - Texts in applied mathematics v. 2 .
Includes index
Includes bibliographical references and index.
Equilibrium Solutions, Stability, and Linearized Stability -- Liapunov Functions -- Invariant Manifolds: Linear and Nonlinear Systems -- Periodic Orbits -- Vector Fields Possessing an Integral -- Index Theory -- Some General Properties of Vector Fields: Existence, Uniqueness, Differentiability, and Flows -- Asymptotic Behavior -- The Poincare-Bendixson Theorem -- Poincare Maps -- Conjugacies of Maps, and Varying the Cross-Section -- Structural Stability, Genericity, and Transversality -- Lagrange's Equations -- Hamiltonian Vector Fields -- Gradient Vector Fields -- Reversible Dynamical Systems -- Asymptotically Autonomous Vector Fields -- Center Manifolds -- Normal Forms -- Bifurcation of Fixed Points of Vector Fields -- Bifurcations of Fixed Points of Maps -- On the Interpretation and Application of Bifurcation Diagrams: A Word of Caution -- The Smale Horseshoe -- Symbolic Dynamics -- The Conley -- Moser Conditions, or "How to Prove That a Dynamical System is Chaotic" -- Dynamics Near Homoclinic Points of Two-Dimensional Maps -- Orbits Homoclinic to Hyperbolic Fixed Points in Three-Dimensional Autonomous Vector Fields -- Melnikov's Method for Homoclinic Orbits in Two-Dimensional, Time-Periodic Vector Fields -- Liapunov Exponents -- Chaos and Strange Attractors -- Hyperbolic Invariant Sets: A Chaotic Saddle -- Long Period Sinks in Dissipative Systems and Elliptic Islands in Conservative Systems -- Global Bifurcations Arising from Local Codimension -- Two Bifurcations.
This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos.
9780387001777
2002042742
Differentiable dynamical systems
Sistemas dinámicos diferenciables
Nonlinear theories
Chaotic behavior in systems
QA614.8 / .W544 2003
515.352
Introduction to applied nonlinear dynamical systems and chaos / Stephen Wiggins. - Second edition - xix, 843 pages : illustrations ; 25 cm. - Texts in applied mathematics v. 2 .
Includes index
Includes bibliographical references and index.
Equilibrium Solutions, Stability, and Linearized Stability -- Liapunov Functions -- Invariant Manifolds: Linear and Nonlinear Systems -- Periodic Orbits -- Vector Fields Possessing an Integral -- Index Theory -- Some General Properties of Vector Fields: Existence, Uniqueness, Differentiability, and Flows -- Asymptotic Behavior -- The Poincare-Bendixson Theorem -- Poincare Maps -- Conjugacies of Maps, and Varying the Cross-Section -- Structural Stability, Genericity, and Transversality -- Lagrange's Equations -- Hamiltonian Vector Fields -- Gradient Vector Fields -- Reversible Dynamical Systems -- Asymptotically Autonomous Vector Fields -- Center Manifolds -- Normal Forms -- Bifurcation of Fixed Points of Vector Fields -- Bifurcations of Fixed Points of Maps -- On the Interpretation and Application of Bifurcation Diagrams: A Word of Caution -- The Smale Horseshoe -- Symbolic Dynamics -- The Conley -- Moser Conditions, or "How to Prove That a Dynamical System is Chaotic" -- Dynamics Near Homoclinic Points of Two-Dimensional Maps -- Orbits Homoclinic to Hyperbolic Fixed Points in Three-Dimensional Autonomous Vector Fields -- Melnikov's Method for Homoclinic Orbits in Two-Dimensional, Time-Periodic Vector Fields -- Liapunov Exponents -- Chaos and Strange Attractors -- Hyperbolic Invariant Sets: A Chaotic Saddle -- Long Period Sinks in Dissipative Systems and Elliptic Islands in Conservative Systems -- Global Bifurcations Arising from Local Codimension -- Two Bifurcations.
This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos.
9780387001777
2002042742
Differentiable dynamical systems
Sistemas dinámicos diferenciables
Nonlinear theories
Chaotic behavior in systems
QA614.8 / .W544 2003
515.352