Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of certain smooth one-dimensional mappings IV: Asymptotic
  geometry of Cantor sets   We study hyperbolic mappings depending on a parameter $\varepsilon $. Each of
them has an invariant Cantor set. As $\varepsilon $ tends to zero, the mapping
approaches the boundary of hyperbolicity. We analyze the asymptotics of the gap
geometry and the scaling function geometry of the invariant Cantor set as
$\varepsilon $ goes to zero. For example, in the quadratic case, we show that
all the gaps close uniformly with speed $\sqrt {\varepsilon}$. There is a
limiting scaling function of the limiting mapping and this scaling function has
dense jump discontinuities because the limiting mapping is not expanding.
Removing these discontinuities by continuous extension, we show that we obtain
the scaling function of the limiting mapping with respect to the Ulam-von
Neumann type metric.

34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org