Portugaliae Mathematica


Full-Text PDF (218 KB) | Metadata | Table of Contents | PM summary
Volume 68, Issue 1, 2011, pp. 1–17
DOI: 10.4171/PM/1878

Published online: 2011-03-06

Denseness of ergodicity for a class of volume-preserving flows

Mário Bessa[1] and Jorge Rocha[2]

(1) Universidade do Porto, Portugal
(2) Universidade do Porto, Portugal

We consider the class of $C^1$ partially hyperbolic volume-preserving flows with one-dimensional central direction endowed with the $C^1$-Whitney topology. We prove that, within this class, any flow can be approximated by an ergodic $C^2$ volume-preserving flow and so, as a consequence, ergodicity is dense.

Keywords: Dominated splitting, partial hyperbolicity, volume-preserving flows, Lyapunov exponents, stable ergodicity

Bessa Mário, Rocha Jorge: Denseness of ergodicity for a class of volume-preserving flows. Port. Math. 68 (2011), 1-17. doi: 10.4171/PM/1878