Dynamics of $C^1$-diffeomorphisms: global description and prospects for classification

Abstract

We are interested in finding a dense part of the space of $C^1$-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).

References in corpus (2)

• Lyapunov stable chain recurrent classes
• Maps close to identity and universal maps in the Newhouse domain

Cited by in corpus (1)

• On the dominated splitting of Lyapunov stable aperiodic classes