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