Divergent on average directions of Teichmuller geodesic flow
Paul Apisa, Howard Masur
TL;DR
This paper investigates the behavior of directions in quadratic differentials under Teichmuller geodesic flow, revealing that the set of directions diverging on average has Hausdorff dimension exactly one-half.
Contribution
It establishes the precise Hausdorff dimension of the set of diverging directions, advancing understanding of Teichmuller dynamics.
Findings
Set of diverging directions has Hausdorff dimension 0.5
Provides exact measure of divergence behavior in Teichmuller flow
Enhances geometric understanding of quadratic differentials
Abstract
The set of directions from a quadratic differential that diverge on average under Teichmuller geodesic flow has Hausdorff dimension exactly equal to one-half.
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