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April  2000, 6(2): 351-360. doi: 10.3934/dcds.2000.6.351

Examples of topologically transitive skew-products

Viorel Nitica 1,

1. 

Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania

Received  March 1999 Revised  September 1999 Published  January 2000

Let $\sigma:\Sigma\to\Sigma$ be a topologically mixing shift of finite type. If $G$ is a group, and $\beta:\Sigma\to G$ is a continuous function, denote by $\sigma_\beta$ the skew-product of $\sigma$ by $\beta$. If $G$ is $\mathbb R^n$, we show examples of continuous multiparameters families of functions $\beta$ for which the skew-products $\sigma_\beta$ are topologically transitive for sets of parameters of full measure. If $G$ is a connected semisimple matrix Lie group, we show examples of functions $\beta$ for which the skew-products $\sigma_beta$ are topologically transitive.
Keywords: non-compact fiber., skew-products, Topological transitivity.
Mathematics Subject Classification: 58F1.
Citation: Viorel Nitica. Examples of topologically transitive skew-products. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 351-360. doi: 10.3934/dcds.2000.6.351
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