Dynamical Systems: Stability, Symbolic Dynamics, and Chaos 2nd Edition (Studies in Advanced Mathematics)

Several distinctive aspects make Dynamical Systems unique, including: treating the subject from a mathematical perspective with the proofs of most of the results includedproviding a careful review of background materialsintroducing ideas through examples and at a level accessible to a beginning graduate studentfocusing on multidimensional systems of real variablesThe 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.