Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of Rare Events Point Processes to the Poisson for billiards   We show that for planar dispersing billiards the return times distribution
is, in the limit, Poisson for metric balls almost everywhere w.r.t. the SRB
measure. Since the Poincar\'e return map is piecewise smooth but becomes
singular at the boundaries of the partition elements, recent results on the
limiting distribution of return times cannot be applied as they require the
maps to have bounded second derivatives everywhere. We first prove the Poisson
limiting distribution assuming exponentially decaying correlations. For the
case when the correlations decay polynomially, we induce on a subset on which
the induced map has exponentially decaying correlations. We then prove a
general theorem according to which the limiting return times statistics of the
original map and the induced map are the same.

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The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an