Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symbolic dynamics for surface diffeomorphisms with positive topological
  entropy   Suppose f is a C^{1+\epsilon} surface diffeomorphism with positive
topological entropy. For every positive \delta strictly smaller than the
topological entropy of f we construct an invariant Borel set E such that (a)
f|E has a countable Markov partition; and (b) E has full measure with respect
to any ergodic invariant probability measure with entropy larger than \delta.
This allows us to prove the following conjecture of A. Katok: if f is C^\infty
with topological entropy h>0, and if P_n(f)=#{x:f^n(x)=x}, then limsup
P_n(f)/exp(nh)>0.

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The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int