Diophantine approximation by orbits of Markov maps
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2011
- DOI:
- 10.48550/arXiv.1111.1081
- arXiv:
- arXiv:1111.1081
- Bibcode:
- 2011arXiv1111.1081L
- Keywords:
-
- Mathematics - Dynamical Systems;
- Mathematics - Classical Analysis and ODEs;
- Mathematics - Number Theory;
- 37AXX;
- 11K60;
- 28A78
- E-Print:
- 24 pages, 3 figures