Dynamical properties of the absolute period foliation
Ursula Hamenstaedt
TL;DR
This paper proves the ergodicity of the absolute period foliation in the principal stratum of abelian differentials for genus at least 3 and explores its properties in affine invariant manifolds.
Contribution
It establishes the ergodic nature of the absolute period foliation in a significant moduli space and investigates its structure within affine invariant manifolds.
Findings
Proves ergodicity of the absolute period foliation for genus ≥ 3
Analyzes the structure of the foliation in affine invariant manifolds
Provides new insights into the dynamics of abelian differentials
Abstract
We show that the absolute period foliation of the principal stratum of abelian differentials on a surface of genus at least 3 is ergodic. We also investigate the absolute period foliation of affine invariant manifolds.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Geometric Analysis and Curvature Flows