On the persistence of invariant curves for Fibered Holomorphic Transformations
Dynamical Systems
2015-05-13 v1
Abstract
We consider the problem of the persistence of invariant curves for analytical fibered holomorphic transformations. We define a fibered rotation number associated to an invariant curve. We show that an invariant curve with a prescribed fibered rotation number persists under small perturbations on the dynamics provided that the pair of rotation numbers verifies a Brjuno type arithmetical condition.
Keywords
Cite
@article{arxiv.0801.2549,
title = {On the persistence of invariant curves for Fibered Holomorphic Transformations},
author = {Mario Ponce},
journal= {arXiv preprint arXiv:0801.2549},
year = {2015}
}