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# Examples of topologically transitive skew-products

• 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.
Mathematics Subject Classification: 58F15.

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