Topological Attractors of Contracting Lorenz Maps
Abstract
We study the nonwandering set of contracting Lorenz maps. We show that if such a map $f$ doesn't have any attracting periodic orbit, then there is a unique topological attractor. Precisely, there is a compact set $\Lambda$ such that $\omega_f(x)=\Lambda$ for a residual set of points $x \in [0,1]$. Furthermore, we classify the possible kinds of attractors that may occur.
 Publication:

arXiv eprints
 Pub Date:
 November 2016
 arXiv:
 arXiv:1612.00093
 Bibcode:
 2016arXiv161200093B
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
 arXiv admin note: substantial text overlap with arXiv:1402.2862