Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Genericity of contracting elements in groups   In this paper, we establish that, for statistically convex-cocompact actions,
contracting elements are exponentially generic in counting measure. Among
others, the following exponential genericity results are obtained as
corollaries for the set of hyperbolic elements in relatively hyperbolic groups,
the set of rank-1 elements in CAT(0) groups, and the set of pseudo-Anosov
elements in mapping class groups.
  Regarding a proper action, the set of non-contracting elements is proven to
be growth-negligible. In particular, for mapping class groups, the set of
pseudo-Anosov elements is generic in a sufficiently large subgroup, provided
that the subgroup has purely exponential growth. By Roblin's work, we obtain
that the set of hyperbolic elements is generic in any discrete group action on
CAT(-1) space with finite BMS measure.
  Applications to the number of conjugacy classes of non-contracting elements
are given for non-rank-1 geodesics in CAT(0) groups with rank-1 elements.

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The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: nlin
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph