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Zbl 1156.37322
Rudnicki, Ryszard
Chaos for some infinite-dimensional dynamical systems. (English)
[J] Math. Methods Appl. Sci. 27, No. 6, 723-738 (2004). ISSN 0170-4214; ISSN 1099-1476/e

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 2000:: *37L05 General theory, nonlinear semigroups, evolution equations
37B05 Transformations and group actions with special properties
37L30 Attractors and their dimensions
37L40 Invariant measures
35B41 Attractors
35B99 Qualitative properties of solutions of PDE

Keywords: chaos; invariant measure; partial differential equations; infinite-dimensional semiflow

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