Diophantine approximation by orbits of Markov maps - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2011

Diophantine approximation by orbits of Markov maps

Résumé

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.

Dates et versions

hal-00795540 , version 1 (28-02-2013)

Identifiants

Citer

Lingmin Liao, Stephane Seuret. Diophantine approximation by orbits of Markov maps. 2011. ⟨hal-00795540⟩
82 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More