Symbolic dynamics for three-dimensional flows with positive topological entropy

By Yuri Lima, O. Sarig. Journal of the European Mathematical Society (Print), 2014

62 citations recorded by the source corpus.

We construct symbolic dynamics on sets of full measure (w.r.t. an ergodic measure of positive entropy) for $C^{1+\epsilon}$ flows on compact smooth three-dimensional manifolds. One consequence is that the geodesic flow on the unit tangent bundle of a compact $C^\infty$ surface has at least const $\times(e^{hT}/T)$ simple closed orbits of period less than $T$, whenever the topological entropy $h$ is positive -- and without further assumptions on the curvature.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7c6aa444d7d3f9e5db5d769c08a05ba931c4be70

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In Applied Mathematics

In Mathematical Physics

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Citations in the corpus

Unique equilibrium states for geodesic flows in nonpositive curvature (2017, methodology): “It follows from work of Ledrappier, Lima, and Sarig [18, 17] that these equilibrium states are Bernoulli, see §9.”
Measures of maximal entropy for surface diffeomorphisms (2018, background): “Combining with [62, 59], some of our results should extend to non-singular flows on three-dimensional manifolds, and in particular to the geodesic flows of positive topological entropy on surface.”