English

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 C1C^1-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).

Keywords

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}
}
R2 v1 2026-06-22T04:04:24.699Z