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arXiv · 1911.00206

Symbolic extensions for 3-dimensional diffeomorphisms

David Burguet·Gang Liao
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Abstract

We prove that every $\mathcal{C}^{r}$ diffeomorphism with $r>1$ 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.

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David Burguet, Gang Liao. 2019-11-01. Symbolic extensions for 3-dimensional diffeomorphisms. https://arxiv.org/abs/1911.00206

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