The centralizer of Komuro-expansive flows and expansive R^d-actions

2016/04/22 by Bonomo, Wescley, Rocha, Jorge, Varandas, Paulo
#37C10 #37C85 #37D20 #37D25 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.06516

Abstract

In this paper we study the centralizer of flows and \mathbb R^d-actions on compact Riemannian manifolds. We prove that the centralizer of every C^∞ Komuro-expansive flow with non-ressonant singularities is trivial, meaning it is the smallest possible, and deduce there exists an open and dense subset of geometric Lorenz attractors with trivial centralizer. We show that \mathbb R^d-actions obtained as suspension of \mathbb Z^d-actions are expansive if and only if the same holds for the \mathbb Z^d-actions. We also show that homogeneous expansive \mathbb R^d-actions have quasi-trivial centralizers, meaning that it consists of orbit invariant, continuous linear reparametrizations of the \mathbb R^d-action. In particular, homogeneous Anosov \mathbb R^d-actions have quasi-trivial centralizer.

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