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.

The second edition of this popular text continues to treat dynamical systems from a mathematical perspective centering on multidimensional systems of real variables. At a level accessible to beginning graduate students, it addresses the dynamics of both the iteration of functions and solutions of ordinary differential equations. This edition includes material on horsehoes, an additional chapter on Hamiltonian systems, a revised discussion of the saddle node bifurcation, and proof of the ergodicity of a hyperbolic toral automorphism. Numerous exercises help readers understand the theorems presented and master the techniques of the proofs and topics under consideration. &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 REVIEWSIntroductionOne Dimensional Dynamics by IterationChaos and ItslÃ|