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

2023/07/16 by Pathak, Aritro
#Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2307.08126

Abstract

Starting with a trivial periodic flow on \mathbbSM, 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 \mathbbSM 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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