English

Stable minimality of expanding foliations

Dynamical Systems 2020-05-15 v4

Abstract

We prove that generically in Diffm1(M)\text{Diff}^{1}_{m}(M), if an expanding ff-invariant foliation WW of dimension uu is minimal and there is a periodic point of unstable index uu, the foliation is stably minimal. By this we mean there is a C1C^{1}-neighborhood U\mathcal{U} of ff such that for all C2C^{2}-diffeomorphisms gUg\in \mathcal{U}, the gg-invariant analytic continuation of WW is minimal. In particular, all such gg are topologically mixing. Moreover, all such gg have a hyperbolic ergodic component of the volume measure mm which is essentially dense. This component is, in fact, Bernoulli. We provide new examples of stably minimal diffeomorphisms which are not partially hyperbolic.

Keywords

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

R2 v1 2026-06-23T10:55:42.286Z