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arXiv · 1406.6785

On Shrinking Targets for Piecewise Expanding Interval Maps

Tomas Persson·Michał Rams
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Abstract

For a map $T \colon [0,1] \to [0,1]$ with an invariant measure $\mu$, we study, for a $\mu$-typical $x$, the set of points $y$ such that the inequality $|T^n x - y| < r_n$ is satisfied for infinitely many $n$. We give a formula for the Hausdorff dimension of this set, under the assumption that $T$ is piecewise expanding and $\mu_\phi$ is a Gibbs measure. In some cases we also show that the set has a large intersection property.

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Tomas Persson, Michał Rams. 2014-06-26. On Shrinking Targets for Piecewise Expanding Interval Maps. https://arxiv.org/abs/1406.6785

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