Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A strong Borel--Cantelli lemma for recurrence   Consider a mixing dynamical systems $([0,1], T, \mu)$, for instance a
piecewise expanding interval map with a Gibbs measure $\mu$. Given a
non-summable sequence $(m_k)$ of non-negative numbers, one may define $r_k (x)$
such that $\mu (B(x, r_k(x)) = m_k$. It is proved that for almost all $x$, the
number of $k \leq n$ such that $T^k (x) \in B_k (x)$ is approximately equal to
$m_1 + \ldots + m_n$. This is a sort of strong Borel--Cantelli lemma for
recurrence.
  A consequence is that \[
  \lim_{r \to 0} \frac{\log \tau_{B(x,r)} (x)}{- \log \mu (B (x,r))}
  = 1 \] for almost every $x$, where $\tau$ is the return time.

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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: stat