On generic $G$-prevalent properties of $C^{r}$ diffeomorphisms of $\mathbf{S}^{1}$ and a quantitative K-S theorem
Dynamical Systems
2009-12-25 v1
Abstract
We will consider a convex unbounded set and certain group of actions on this set. This will substitute the translation (by adding) structure usually consider in the classical setting of prevalence. In this way we will be able to define the meaning of -prevalent set. In this setting we will show a kind of quantitative Kupka-Smale Theorem and also a result about rotation numbers which was first consider by J.-C. Yoccoz (and, also by M. Tsujii).
Keywords
Cite
@article{arxiv.0912.4855,
title = {On generic $G$-prevalent properties of $C^{r}$ diffeomorphisms of $\mathbf{S}^{1}$ and a quantitative K-S theorem},
author = {Elismar R. Oliveira and Artur O. Lopes},
journal= {arXiv preprint arXiv:0912.4855},
year = {2009}
}