Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On invariant measures of finite affine type tilings   In this paper, we consider tilings of the hyperbolic 2-space, built with a
finite number of polygonal tiles, up to affine transformation. To such a tiling
T, we associate a space of tilings: the continuous hull Omega(T) on which the
affine group acts. This space Omega(T) inherits a solenoid structure whose
leaves correspond to the orbits of the affine group. First we prove the finite
harmonic measures of this laminated space correspond to finite invariant
measures for the affine group action. Then we give a complete combinatorial
description of these finite invariant measures. Finally we give examples with
an arbitrary number of ergodic invariant probability measures.

15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph