Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Natural extensions of unimodal maps: virtual sphere homeomorphisms and
  prime ends of basin boundaries   Let $\{f_t\colon I\to I\}$ be a family of unimodal maps with topological
entropies $h(f_t)>\frac12\log 2$, and
${\widehat{f}}_t\colon{\widehat{I}}_t\to{\widehat{I}}_t$ be their natural
extensions, where ${\widehat{I}}_t=\varprojlim(I,f_t)$. Subject to some
regularity conditions, which are satisfied by tent maps and quadratic maps, we
give a complete description of the prime ends of the Barge-Martin embeddings of
${\widehat{I}}_t$ into the sphere. We also construct a family $\{\chi_t\colon
S^2\to S^2\}$ of sphere homeomorphisms with the property that each $\chi_t$ is
a factor of ${\widehat{f}}_t$, by a semi-conjugacy for which all fibers except
one contain at most three points, and for which the exceptional fiber carries
no topological entropy: that is, unimodal natural extensions are virtually
sphere homeomorphisms. In the case where $\{f_t\}$ is the tent family, we show
that $\chi_t$ is a generalized pseudo-Anosov map for the dense set of
parameters for which $f_t$ is post-critically finite, so that $\{\chi_{t}\}$ is
the completion of the unimodal generalized pseudo-Anosov family introduced in
[21].

31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th