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arXiv · 2312.10533

Interval Translation Maps with Weakly Mixing Attractors

Henk Bruin·Silvia Radinger
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Abstract

We study linear recurrence and weak mixing of a two-parameter family of interval translation maps $T_{\alpha,\beta}$ for the subset of parameter space where $T_{\alpha,\beta}$ has a Cantor attractor. For this class, there is a procedure similar to the Rauzy induction which acts as a dynamical system $G$ on parameter space, which was used previously to decide whether $T_{\alpha,\beta}$ has an attracting Cantor set, and if so, whether $T_{\alpha,\beta}$ is uniquely ergodic. In this paper we use properties of $G$ to decide whether $T_{\alpha,\beta}$ is linearly recurrent or weak mixing.

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Henk Bruin, Silvia Radinger. 2023-12-16. Interval Translation Maps with Weakly Mixing Attractors. https://arxiv.org/abs/2312.10533

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