Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability for quasi-periodically perturbed Hill's equations   We consider a perturbed Hill's equation of the form $\ddot \phi +
  (p_{0}(t) + \epsilon p_{1}(t)) \phi = 0$, where $p_{0}$ is real analytic and
periodic, $p_{1}$ is real analytic and quasi-periodic and $\eps$ is a ``small''
real parameter. Assuming Diophantine conditions on the frequencies of the
decoupled system, i.e. the frequencies of the external potentials $p_{0}$ and
$p_{1}$ and the proper frequency of the unperturbed ($\epsilon=0$) Hill's
equation, but without making non-degeneracy assumptions on the perturbing
potential $p_{1}$, we prove that quasi-periodic solutions of the unperturbed
equation can be continued into quasi-periodic solutions if $\epsilon$ lies in a
Cantor set of relatively large measure in $[-\epsilon_0,\epsilon_0]$, where
$\epsilon_0$ is small enough. Our method is based on a resummation procedure of
a formal Lindstedt series obtained as a solution of a generalized Riccati
equation associated to Hill's problem.

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The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas