Dynamics of skew products of interval maps

L. S. Efremova

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 72 (2017) no. 1, pp. 101-178

Résumé

In the study of dynamical systems in the class of skew products, the present paper involves the direction most closely connected with advances in one-dimensional dynamics. The main results obtained over the last decades on the dynamics of skew products of interval maps are surveyed. Included here are new results on the structure of the non-wandering set and the centre for $C^1$-smooth skew products of interval maps that are endomorphisms whose quotient maps have complicated dynamics. These results are used to describe the space of skew products of this type. Bibliography: 125 titles.

Détail

Keywords: skew product of interval maps, non-wandering set, depth of the centre, stability as a whole of a family of fibre maps, $\Omega$-stability, dense stability as a whole of a family of fibre maps.
Mots-clés : centre

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