Dynamical Systems Stability, Symbolic Dynamics, and Chaos

This new text/reference treats dynamical systems from a mathematical perspective, centering on multidimensional systems of real variables. Background material is carefully reviewed as it is used throughout the book, & ideas are introduced through examples. Numerous exercises help the reader understand presented theorems & master the techniques of the proofs & topic under consideration. The book treats the dynamics of both iteration of functions & 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. A proof of the existence & continuity of solutions with respect to initial conditions is included. Explicit formulas for the various bifurcations are included, & a treatment of the HTnon map & the Melnikov method is provided. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. Even the more local theory which is treated deals with characterizing types of solutions under various hypothesis. Later chapters deal more directly with more global aspects, with one chapter discussing various examples & later chapters giving the global theory.Robinson, Clark is the author of 'Dynamical Systems Stability, Symbolic Dynamics, and Chaos' with ISBN 9780849384936 and ISBN 0849384931.