English

Symbolic extensions for 3-dimensional diffeomorphisms

Dynamical Systems 2019-11-12 v2

Abstract

We prove that every Cr\mathcal{C}^{r} diffeomorphism with r>1r>1 on a three-dimensional manifold admits symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. This answers positively a conjecture of Downarowicz and Newhouse in dimension three.

Keywords

Cite

@article{arxiv.1911.00206,
  title  = {Symbolic extensions for 3-dimensional diffeomorphisms},
  author = {David Burguet and Gang Liao},
  journal= {arXiv preprint arXiv:1911.00206},
  year   = {2019}
}
R2 v1 2026-06-23T12:01:51.358Z