Discrete orbits, recurrence and solvable subgroups of Diff(C^2,0)
Abstract
We discuss the local dynamics of a subgroup of Diff(C^2,0) possessing locally discrete orbits as well as the structure of the recurrent set for more general groups. It is proved, in particular, that a subgroup of Diff(C^2,0) possessing locally discrete orbits must be virtually solvable. These results are of considerable interest in problems concerning integrable systems.
Cite
@article{arxiv.1406.0461,
title = {Discrete orbits, recurrence and solvable subgroups of Diff(C^2,0)},
author = {Julio C. Rebelo and Helena Reis},
journal= {arXiv preprint arXiv:1406.0461},
year = {2015}
}
Comments
The first version of this paper and "A note on integrability and finite orbits for subgroups of Diff(C^n,0)" are an expanded version of our paper "Discrete orbits and special subgroups of Diff(C^n,0)". An intermediate version re-submitted to the journal on March 2015 is available at http://www.fep.up.pt/docentes/hreis/publications.htm where there is also a comparison between these 3 versions