×

Chaos for some infinite-dimensional dynamical systems. (English) Zbl 1156.37322

Summary: This paper is devoted to the problem of chaotic behaviour of infinite-dimensional dynamical systems. We give a survey of different approaches to study of chaotic behaviour of dynamical systems. We mainly discuss the ergodic-theoretical approach to chaos which bases on the existence of invariant measures having strong analytic and mixing properties. This method is applied to study chaotic behaviour of semiflows generated by semilinear partial differential equations and linear transformations.

MSC:

37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
37L40 Invariant measures for infinite-dimensional dissipative dynamical systems
35B41 Attractors
35B99 Qualitative properties of solutions to partial differential equations
PDFBibTeX XMLCite
Full Text: DOI