English

Codimension one generic homoclinic classes with interior

Dynamical Systems 2009-11-10 v3

Abstract

We study generic diffeomorphisms with a homoclinc class with non empty interior and in particular those admitting a codimension one dominated splitting. We prove that if in the finest dominated splitting the extreme subbundles are one dimensional then the diffeomorphism is partially hyperbolic and from this we deduce that the diffeomorphism is transitive.

Keywords

Cite

@article{arxiv.0806.3036,
  title  = {Codimension one generic homoclinic classes with interior},
  author = {Rafael Potrie and Martin Sambarino},
  journal= {arXiv preprint arXiv:0806.3036},
  year   = {2009}
}

Comments

12 pages, Some corrections

R2 v1 2026-06-21T10:52:09.159Z