Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric measures for hyperbolic sets on surfaces   We present a moduli space for all hyperbolic basic sets of diffeomorphisms on
surfaces that have an invariant measure that is absolutely continuous with
respect to Hausdorff measure. To do this we introduce two new invariants: the
measure solenoid function and the cocycle-gap pair. We extend the eigenvalue
formula of A. N. Livsic and Ja. G. Sinai for Anosov diffeomorphisms which
preserve an absolutely continuous measure to hyperbolic basic sets on surfaces
which possess an invariant measure absolutely continuous with respect to
Hausdorff measure. We characterise the Lipschitz conjugacy classes of such
hyperbolic systems in a number of ways, for example, in terms of eigenvalues of
periodic points and Gibbs measures.

15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th