TY  - BOOK
AU  - Stephen Wiggins
TI  - Introduction to applied nonlinear dynamical systems and chaos
T2  - Texts in Applied Mathematics 
SN  - 9780387001777
AV  - QA614.8 
PY  - 2003///]
CY  - Heidelberg
PB  - Springer-Verlag
KW  - Dynamical system
KW  - Nonlinear dynamics
N1  - Introduction
1. Equilibrium Solutions, Stability, and Linearized Stability
2. Liapunov Functions
3. Invariant Manifolds: Linear and Nonlinear Systems
4. Periodic Orbits
5. Vector Fields Possessing an Integral
6. Index Theory
7. Some General Properties of Vector Fields: Existence, Uniqueness, Differentiability, and Flows
8. Asymptotic Behavior
9. The Poincaré-Bendixson Theorem
10. Poincaré Maps
11. Conjugacies of Maps, and Varying the Cross-Section
12. Structural Stability, Genericity, and Transversality
13. Lagrange’s Equations
14. Hamiltonian Vector Fields
15. Gradient Vector Fields
16. Reversible Dynamical Systems
17. Asymptotically Autonomous Vector Fields
18. Center Manifolds
19. Normal Forms
20. Bifurcation of Fixed Points of Vector Fields
21. Bifurcations of Fixed Points of Maps
22. On the Interpretation and Application of Bifurcation Diagrams: A Word of Caution
23. The Smale Horseshoe
24. Symbolic Dynamics
25. The Conley-Moser Conditions, or “How to Prove That a Dynamical System is Chaotic”
26. Dynamics Near Homoclinic Points of Two-Dimensional Maps
27. Orbits Homoclinic to Hyperbolic Fixed Points in Three-Dimensional Autonomous Vector Fields
28. Melnikov–s Method for Homoclinic Orbits in Two-Dimensional, Time-Periodic Vector Fields
29. Liapunov Exponents
30. Chaos and Strange Attractors
31. Hyperbolic Invariant Sets: A Chaotic Saddle
32. Long Period Sinks in Dissipative Systems and Elliptic Islands in Conservative Systems
33. Global Bifurcations Arising from Local Codimension—Two Bifurcations
N2  - Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in - search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as nume- cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. --- summary provided by publisher
UR  - https://link.springer.com/book/10.1007/b97481?page=2#keywords
ER  -