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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:
37L05General theory, nonlinear semigroups, evolution equations
37B05Transformations and group actions with special properties
37L30Attractors and their dimensions, Lyapunov exponents
37L40Invariant measures (infinite-dimensional dissipative systems)
35B41Attractors (PDE)
35B99Qualitative properties of solutions of PDE