Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flexibility of measure-theoretic entropy of boundary maps associated to
  Fuchsian groups   Given a closed, oriented, compact surface $S$ of constant negative curvature
and genus $g \ge 2$, we study the measure-theoretic entropy of the Bowen-Series
boundary map with respect to its smooth invariant measure. We obtain an
explicit formula for the entropy that only depends on the perimeter of the
$(8g-4)$-sided fundamental polygon of the surface $S$ and its genus. Using
this, we analyze how the entropy changes in the Teichm\"uller space of $S$ and
prove the following flexibility result: the measure-theoretic entropy takes all
values between $0$ and a maximum that is achieved on the surface that admits a
regular $(8g-4)$-sided fundamental polygon. We also compare the
measure-theoretic entropy to the topological entropy of these maps and show
that the smooth invariant measure is not the measure of maximal entropy.

21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat