Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative recurrence properties in conformal iterated function
  systems   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 $$R(f):=\{x\in J^\ast:
|T^nx-x|<e^{-S_n f(x)}, \ {\text{for infinitely many}}\ n\in \mathbb{N}\},$$
where $S_n f(x)$ is the $n$th Birkhoff sum associated with the potential $f$.
In other words, $R(f)$ contains the points $x$ whose orbits return close to $x$
infinitely often, with a rate varying along time. Under some conditions, we
prove that the Hausdorff dimension of $R(f)$ is given by $\inf\{s\ge 0: P(T,
-s(f+\log |T'|))\le 0\}$, where $P$ is the pressure function and $T'$ is the
derivative of $T$. We present some applications of the main theorem to
Diophantine approximation.

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The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg