Resonant tori of arbitrary codimension for quasi-periodically forced systems
Dynamical Systems
2017-03-07 v1 Classical Analysis and ODEs
Abstract
We consider a system of rotators subject to a small quasi-periodic forcing. We require the forcing to be analytic and satisfy a time-reversibility property and we assume its frequency vector to be Bryuno. Then we prove that, without imposing any non-degeneracy condition on the forcing, there exists at least one quasi-periodic solution with the same frequency vector as the forcing. The result can be interpreted as a theorem of persistence of lower-dimensional tori of arbitrary codimension in degenerate cases.
Keywords
Cite
@article{arxiv.1403.2872,
title = {Resonant tori of arbitrary codimension for quasi-periodically forced systems},
author = {Livia Corsi and Guido Gentile},
journal= {arXiv preprint arXiv:1403.2872},
year = {2017}
}
Comments
20 pages