Topological attractors of contracting Lorenz maps

@article{Brando2018TopologicalAO,
  title={Topological attractors of contracting Lorenz maps},
  author={Paulo Brand{\~a}o},
  journal={Annales de l'Institut Henri Poincar{\'e} C, Analyse non lin{\'e}aire},
  year={2018}
}
  • Paulo Brandão
  • Published 1 December 2016
  • Mathematics, Physics
  • Annales de l'Institut Henri Poincaré C, Analyse non linéaire
We study the non-wandering 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. 

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