English

An example of $C^1$-generically wild homoclinic classes with index deficiency

Dynamical Systems 2011-07-20 v1

Abstract

Given a closed smooth four-dimensional manifold, we construct a diffeomorphism that has a homoclinic class whose continuation locally generically satisfies the following condition: it does not admit any kind of dominated splittings whereas any periodic points belonging to it never have unstable index one.

Keywords

Cite

@article{arxiv.1006.5569,
  title  = {An example of $C^1$-generically wild homoclinic classes with index deficiency},
  author = {Katsutoshi Shinohara},
  journal= {arXiv preprint arXiv:1006.5569},
  year   = {2011}
}