Dynamical Systems Stability, Symbolic Dynamics, and Chaos
Several distinctive aspects make Dynamical Systems unique, including:
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.
One Dimensional Dynamics by Iteration
Chaos and Its Measurement
Analysis near Fixed Points and Periodic Orbits
Bifurcation of Periodic Points
Examples of Hyperbolic Sets and Attractors
Measurement of Chaos in Higher Dimensions
Global Theory of Hyperbolic Systems
Smoothness of Stable Manifolds and Applications
"…was impressed with the teachability of this text and with the exercises at the end of each chapter, which seemed be nicely graded in difficulty."
-D. Givoli, APPLIED MECHANICS REVIEWS