Survey of Nonlinear Dynamics (Chaos Theory).

摘要

The aim of this report is to give a survey of the whole field of nonlinear dynamics (chaos theory) in compressed form. The standard topics--such as stability and bifurcation of continuous and discrete time systems, Hamiltonian systems, measures of chaos through Lyapunov exponents, broad band power spectra, and algorithmic complexity and related entropies, and experimental realization of chaos ---are covered. But in addition, some topics seldom seen in short surveys are included: basic sensitive dependence and a precise definition of chaos, absence of chaos in a large sector of quantum mechanics, renormalization group and critical phenomena theory, and the very important Galerkin approximation method in partial differential equation dynamics. Throughout the report mathematical rigor is not emphasized; however, precise statements of the crucial, mainly topological, key concepts and theorems are insisted upon.