English

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 GG 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 GG-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}
}