Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A stretched exponential bound on the rate of growth of the number of
  periodic points for prevalent diffeomorphisms   Let M be a compact manifold of dimension at least 2, Diff^r(M) be the space
of C^r diffeomorphisms of M. Define for any diffeomorphism f in Diff^r(M)
number of isolated periodic points of period n by P_n(f)=# {isolated x in M:
f^n(x)=x}. Artin--Mazur proved that for a dense set of diffeomorphisms the
number of periodic points P_n(f) growth at most exponentially fast in n. The
author proved that there is an open set N \subset Diff^r(M) such that for a
Baire generic set of diffeomorphisms the number of periodic points P_n(f)
growth arbitrarily fast.
  Arnold posed a problem: Prove that diffeomorphisms with at most exponential
growth of the number of periodic points in period have probability one. In this
paper we annonce and exhibit key ingredients for a partial solution to Arnold's
problem: we prove that for any epsilon>0 with probability one the number of
periodic points is bounded by a streched exponential estimate
P_n(f)<exp(Cn^{1+epsilon}).

35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat