Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic likelihood of chaos for smooth families of circle maps   We consider a smooth two-parameter family $f_{a,L}\colon\theta\mapsto
\theta+a+L\Phi(\theta)$ of circle maps with a finite number of critical points.
For sufficiently large $L$ we construct a set $A_L^{(\infty)}$ of $a$-values of
positive Lebesgue measure for which the corresponding $f_{a,L}$ exhibits an
exponential growth of derivatives along the orbits of the critical points. Our
construction considerably improves the previous one of Wang and Young for the
same class of families, in that the following asymptotic estimate holds: the
Lebesgue measure of $A_L^{(\infty)}$ tends to full measure in $a$-space as $L$
tends to infinity.

22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
19
The categories of this paper are: eess
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph