Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equilibrium States for Partially Hyperbolic Horseshoes   In this paper, we study ergodic features of invariant measures for the
partially hyperbolic horseshoe at the boundary of uniformly hyperbolic
diffeomorphisms constructed in \cite{DHRS07}. Despite the fact that the
non-wandering set is a horseshoe, it contains intervals. We prove that every
recurrent point has non-zero Lyapunov exponents and all ergodic invariant
measures are hyperbolic. As a consequence, we obtain the existence of
equilibrium measures for any continuous potential. We also obtain an example of
a family of $C^\infty$ potentials with phase transition.

15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex