Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost-sure quasiperiodicity in countably many co-existing circles   In many dynamical systems, countably infinitely many invariant tori co-exist.
The occurrence of quasiperiodicity on any one of these tori is sometimes
sufficient to establish strong global properties, like dense trajectories and
periodic points. In this paper, we establish sufficient conditions for a
countably infinite collection of parameterized circle diffeomorphisms to have
quasiperiodic behavior on at least one of the circles, for a full Lebesgue
measure set of the parameter values. As an application, we study parameterized
families of skew-product maps on the torus and prove sufficient conditions for
the existence of at least on quasiperiodic circle for Lebesgue-almost every
parameter value.

26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio