On the definition of `chaos'

A. Yu. Kolesov   ; N. Kh. Rozov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 64 (2009) no. 4, pp. 701-744

Résumé

A new definition of a chaotic invariant set is given for a continuous semiflow in a metric space. It generalizes the well-known definition due to Devaney and allows one to take into account a special feature occurring in the non-compact infinite-dimensional case: so-called turbulent chaos. The paper consists of two sections. The first contains several well-known facts from chaotic dynamics, together with new definitions and results. The second presents a concrete example demonstrating that our definition of chaos is meaningful. Namely, an infinite-dimensional system of ordinary differential equations is investigated having an attractor that is chaotic in the sense of the new definition but not in the sense of Devaney or Knudsen. Bibliography: 65 titles.

Détail

Keywords: attractor, topological transitivity, mixing, invariant measure, hyperbolicity.
Mots-clés : chaos

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