English

On the Structure of Lorenz Maps

Dynamical Systems 2014-02-13 v1

Abstract

We study the non-wandering set of C3C^3 contracting Lorenz maps ff with negative Schwarzian derivative. We show that if ff doesn't have attracting periodic orbit, then there is a unique topological attractor. Precisely, there is a transitive compact set Λ\Lambda such that ωf(x)=Λ\omega_f(x)=\Lambda for a residual set of points x[0,1]x \in [0,1]. We also develop in the context of Lorenz maps the classical theory of spectral decomposition constructed for Axiom A maps by Smale.

Keywords

Cite

@article{arxiv.1402.2862,
  title  = {On the Structure of Lorenz Maps},
  author = {Paulo Brandão},
  journal= {arXiv preprint arXiv:1402.2862},
  year   = {2014}
}
R2 v1 2026-06-22T03:06:49.615Z