On the Structure of Lorenz Maps

2014/02/12 by Brandão, Paulo
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1402.2862

Abstract

We study the non-wandering set of C³ contracting Lorenz maps f with negative Schwarzian derivative. We show that if f doesn't have attracting periodic orbit, then there is a unique topological attractor. Precisely, there is a transitive compact set Λ such that ω_f(x)=Λ for a residual set of points x ∈ [0,1]. We also develop in the context of Lorenz maps the classical theory of spectral decomposition constructed for Axiom A maps by Smale.

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