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Pré-Publication, Document De Travail Année : 2013

Quantitative recurrence properties in conformal iterated function systems

Résumé

Let $\Lambda$ be a countable index set and $S=\{\phi_i: i\in \Lambda\}$ be a conformal iterated function system on $[0,1]^d$ satisfying the open set condition. Denote by $J$ the attractor of $S$. With each sequence $(w_1,w_2,...)\in \Lambda^{\mathbb{N}}$ is associated a unique point $x\in [0,1]^d$. Let $J^\ast$ denote the set of points of $J$ with unique coding, and define the mapping $T:J^\ast \to J^\ast$ by $Tx= T (w_1,w_2, w_3...) = (w_2,w_3,...)$. In this paper, we consider the quantitative recurrence properties related to the dynamical system $(J^\ast, T)$. More precisely, let $f:[0,1]^d\to \mathbb{R}^+$ be a positive function and $$R(f):=\{x\in J^\ast: |T^nx-x|

Dates et versions

hal-00911042 , version 1 (28-11-2013)

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Stéphane Seuret, Baowei Wang. Quantitative recurrence properties in conformal iterated function systems. 2013. ⟨hal-00911042⟩
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