The set of periods for a class of skew-products

Jose S. Cánovas; Antonio Falcó

doi:10.3934/dcds.2000.6.893

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2000, Volume 6, Issue 4: 893-900. Doi: 10.3934/dcds.2000.6.893

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The set of periods for a class of skew-products

Jose S. Cánovas^1, and
Antonio Falcó^2,

1.
Departamento de Matemática aplicada y Estadística, Universidad Politécnica de Cartagena, Paseo de Alfonso XIII, 30203 Cartagena(Murcia)
2.
Facultad de Ciencias Sociales y Jurídicas, Campus de Elche, Universidad Cardenal Herrera-CEU, Carrer Comissari 1, 03203 Elx-Elche

Received: February 29, 2000

Revised: June 30, 2000

Published: September 2000

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Abstract

In this paper we give a characterization for the set of periods for a class of skew-products that we can see as deterministic systems driven by some stochastic process. This class coincides with a set of skew product maps from $\Sigma_N \times \mathbb S^1$ into itself, where $\Sigma_N$ is the space of the bi-infinite sequences on $N$ symbols and $\mathbb S^1$ is the unit circle.

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Mathematics Subject Classification: 58F22, 26A18, 58F08.

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