Author	Wiggins, Stephen. author
Title	Introduction to Applied Nonlinear Dynamical Systems and Chaos [electronic resource] / by Stephen Wiggins
Imprint	New York, NY : Springer New York, 2003
Edition	Second Edition
Connect to	http://dx.doi.org/10.1007/b97481
Descript	XXXVIII, 844 p. online resource

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 teaching the techniques and ideas that 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 glossary of terms, making it a 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 -- Some General Properties of Vector Fields: Existence, Uniqueness, Differentiability, and Flows -- Asymptotic Behavior -- The Poincarรฉ-Bendixson Theorem -- Poincarรฉ Maps -- Conjugacies of Maps, and Varying the Cross-Section -- Structural Stability, Genericity, and Transversality -- Lagrangeโs 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 โHow to Prove That a Dynamical System is Chaoticโ -- Dynamics Near Homoclinic Points of Two-Dimensional Maps -- Orbits Homoclinic to Hyperbolic Fixed Points in Three-Dimensional Autonomous Vector Fields -- Melnikovโs 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 CodimensionโTwo Bifurcations -- Glossary of Frequently Used Terms

1. Mathematics
2. Dynamics
3. Ergodic theory
4. Applied mathematics
5. Engineering mathematics
6. Statistical physics
7. Dynamical systems
8. Mathematics
9. Dynamical Systems and Ergodic Theory
10. Applications of Mathematics
11. Statistical Physics
12. Dynamical Systems and Complexity
13. Appl.Mathematics/Computational Methods of Engineering