English

On codimension one partially hyperbolic diffeomorphisms

Dynamical Systems 2022-11-03 v1

Abstract

We show that every codimension one partially hyperbolic diffeomorphism must support on Tn\mathbb{T}^{n}. It is locally uniquely integrable and derived from a linear codimension one Anosov diffeomorphism. Moreover, this system is intrinsically ergodic, and the A. Katok's conjecture about the existence of ergodic measures with intermediate entropies holds for it.

Keywords

Cite

@article{arxiv.2211.01124,
  title  = {On codimension one partially hyperbolic diffeomorphisms},
  author = {Xiang Zhang},
  journal= {arXiv preprint arXiv:2211.01124},
  year   = {2022}
}

Comments

26 pages, 5 figures. Any suggestions and comments are welcome

R2 v1 2026-06-28T05:00:57.544Z