English

Topological properties of Lorenz maps derived from unimodal maps

Dynamical Systems 2019-10-09 v1

Abstract

A symmetric Lorenz map is obtain by ``flipping'' one of the two branches of a symmetric unimodal map. We use this to derive a Sharkovsky-like theorem for symmetric Lorenz maps, and also to find cases where the unimodal map restricted to the critical omega-limit set is conjugate to a Sturmian shift. This has connections with properties of unimodal inverse limit spaces embedded as attractors of some planar homeomorphisms.

Keywords

Cite

@article{arxiv.1910.03361,
  title  = {Topological properties of Lorenz maps derived from unimodal maps},
  author = {Ana Anušić and Henk Bruin and Jernej Činč},
  journal= {arXiv preprint arXiv:1910.03361},
  year   = {2019}
}