Dynamics of $C^1$-diffeomorphisms: global description and prospects for classification
Dynamical Systems
2014-05-05 v1
Abstract
We are interested in finding a dense part of the space of -diffeomorphisms which decomposes into open subsets corresponding to different dynamical behaviors: we discuss results and questions in this direction. In particular we present recent results towards a conjecture by J. Palis: any system can be approximated either by one which is hyperbolic (and whose dynamics is well understood) or by one which exhibits a homoclinic bifurcation (a simple local configuration involving one or two periodic orbits).
Cite
@article{arxiv.1405.0305,
title = {Dynamics of $C^1$-diffeomorphisms: global description and prospects for classification},
author = {Sylvain Crovisier},
journal= {arXiv preprint arXiv:1405.0305},
year = {2014}
}