Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Real entropy rigidity under quasi-conformal deformations   We set up a real entropy function $h_\Bbb{R}$ on the space $\mathcal{M}'_d$
of M\"obius conjugacy classes of real rational maps of degree $d$ by assigning
to each class the real entropy of a representative $f\in\Bbb{R}(z)$; namely,
the topological entropy of its restriction $f\restriction_{\hat{\Bbb{R}}}$ to
the real circle. We prove a rigidity result stating that $h_\Bbb{R}$ is locally
constant on the subspace determined by real maps quasi-conformally conjugate to
$f$. As examples of this result, we analyze real analytic stable families of
hyperbolic and flexible Latt\`es maps with real coefficients along with
numerous families of degree $d$ real maps of real entropy $\log(d)$. The latter
discussion moreover entails a complete classification of maps of maximal real
entropy.

35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys