Stable minimality of expanding foliations
Dynamical Systems
2020-05-15 v4
Abstract
We prove that generically in , if an expanding -invariant foliation of dimension is minimal and there is a periodic point of unstable index , the foliation is stably minimal. By this we mean there is a -neighborhood of such that for all -diffeomorphisms , the -invariant analytic continuation of is minimal. In particular, all such are topologically mixing. Moreover, all such have a hyperbolic ergodic component of the volume measure which is essentially dense. This component is, in fact, Bernoulli. We provide new examples of stably minimal diffeomorphisms which are not partially hyperbolic.
Cite
@article{arxiv.1908.09079,
title = {Stable minimality of expanding foliations},
author = {Gabriel Nuñez and Jana Rodriguez Hertz},
journal= {arXiv preprint arXiv:1908.09079},
year = {2020}
}
Comments
18 pages, 4 figures, edited version, one section with new examples added