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

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.