The centralizer of Komuro-expansive flows and expansive actions

• Type: Article in International Scientific Journal
• Date: 2018

Authors

Bonomo, W (Author) Other; Jorge Rocha (Author) FCUP; Varandas, P (Author) FCUP

Journal

Title: Mathematische Zeitschrift

Vol. 289

Pages: 1059-1088

ISSN: 0025-5874

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 6 Citations

Other information

Authenticus ID: P-00P-2DY

DOI: 10.1007/s00209-017-1988-7

Abstract (EN): In this paper we study the centralizer of flows and -actions on compact Riemannian manifolds. We prove that the centralizer of every Komuro-expansive flow with non-resonant 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 -actions obtained as suspension of -actions are expansive if and only if the same holds for the -actions. We also show that homogeneous expansive -actions have quasi-trivial centralizers, meaning that it consists of orbit invariant, continuous linear reparameterizations of the -action. In particular, homogeneous Anosov -actions have quasi-trivial centralizer.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 30