Symbolic extensions for 3-dimensional diffeomorphisms

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.

References in corpus (1)

• Upper bounds on measure theoretic tail entropy for dominated splittings

Cited by in corpus (1)

• The Symbolic Extension Theory in Topological Dynamics