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arXiv · 2307.08126

Ergodicity of a surgered flow on unit tangent bundle of hyperbolic surface

Aritro Pathak
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Abstract

Starting with a trivial periodic flow on $\mathbb{S}M$, the unit tangent bundle of a genus two surface, we perform a Dehn-type surgery on the manifold around a tubular neighborhood of a curve on $\mathbb{S}M$ that projects to a self-intersecting closed geodesic on $M$, to get a surgered flow which restricted to the surgery region is ergodic with respect to the volume measure. The surgered flow projects to a map on the surgery track that can be taken to be a linked twist map with oppositely oriented shears which generates the ergodic behavior for sufficiently strong shears in the surgery.

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Aritro Pathak. 2023-07-16. Ergodicity of a surgered flow on unit tangent bundle of hyperbolic surface. https://arxiv.org/abs/2307.08126

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