Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-periodic motions in dynamical systems. Review of a renormalisation
  group approach   Power series expansions naturally arise whenever solutions of ordinary
differential equations are studied in the regime of perturbation theory. In the
case of quasi-periodic solutions the issue of convergence of the series is
plagued of the so-called small divisor problem. In this paper we review a
method recently introduced to deal with such a problem, based on
renormalisation group ideas and multiscale techniques. Applications to both
quasi-integrable Hamiltonian systems (KAM theory) and non-Hamiltonian
dissipative systems are discussed. The method is also suited to situations in
which the perturbation series diverges and a resummation procedure can be
envisaged, leading to a solution which is not analytic in the perturbation
parameter: we consider explicitly examples of solutions which are only
infinitely differentiable in the perturbation parameter, or even defined on a
Cantor set.

21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg