This volume is intended for advanced undergraduate or first year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on questions and ideas which will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background such as students in engineering, physics, chemistry and biology, will find this text as useful as students of mathematics. This new edition contains extensive new material on invariant manifold theory and normal forms (in particular, Hamiltonian normal forms and the role of symmetry). Lagrangian, Hamiltonian, gradient, and reversible dynamical systems are also discussed. Elementary Hamiltonian bifurcations are covered, as well as the basic properties of circle maps. The book contains an extensive bibliography, as well as a detailed comprehensive book on applied nonlinear dynamical systems from a geometrical and analytical point of view.
Equilibrium Solutions, Stability, and Linearized Stability * Liapunov Functions * Invariant Manifolds: Linear and Nonlinear Systems * Periodic Orbits * Vector Fields Possessing an Integral * Index theory * General Properties of Vector Fields * 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 * Bifurcations of Fixed Points of Vector Fields * Bifurcations of Fixed Points of Maps * On the Interpolation of Fixed Points of Maps * On the Interpolation of Bifurcation Diagrams * The Smale Horseshoe * Symbolic Dynamics * The Conley-Moser Conditions * Dynamics Near Homoclinic Points of Two-Dimensional Maps * Orbits Homoclinic to Hyperbolic Fixed Points * Melnikov's Method * 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 * Glossary of Frequently Used Terms
(0 Comentarios)
