Dynamical Systems Stability, Symbolic Dynamics, and Chaos [Hardcover]

Several distinctive aspects make Dynamical Systems unique, including:

treating the subject from a mathematical perspective with the proofs of most of the results included

providing a careful review of background materials

introducing ideas through examples and at a level accessible to a beginning graduate student

focusing on multidimensional systems of real variables

The book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. The more local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects.

Introduction
One Dimensional Dynamics by Iteration
Chaos and Its Measurement
Linear Systems
Analysis near Fixed Points and Periodic Orbits
Hamiltonian Systems
Bifurcation of Periodic Points
Examples of Hyperbolic Sets and Attractors
Measurement of Chaos in Higher Dimensions
Global Theory of Hyperbolic Systems
Generic Properties
Smoothness of Stable Manifolds and Applications