Diophantine approximation by orbits of Markov maps

Details Diophantine approximation by orbits of Markov maps Diophantine approximation by orbits of Markov maps

2011-11-04

arxiv.org/abs/1111.1081v1

Mathematics

Dynamical Systems

24 pages, 3 figures; To appear in ETDS, 2011

Scientific paper

In 1995, Hill and Velani introduced the shrinking targets theory. Given a dynamical system $([0,1],T)$, they investigated the Hausdorff dimension of sets of points whose orbits are close to some fixed point. In this paper, we study the sets of points well-approximated by orbits $\{T^n x\}_{n\geq 0}$, where $T$ is an expanding Markov map with a finite partition supported by $[0,1]$. The dimensions of these sets are described using the multifractal properties of invariant Gibbs measures.

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