Billiards in L-shaped tables with barriers
Matt Bainbridge
TL;DR
This paper calculates the volume of specific eigenform loci in genus two moduli space and uses this to derive asymptotic formulas for counting closed billiard paths in L-shaped polygons with barriers.
Contribution
It introduces a method to connect eigenform volume calculations with counting problems in billiards within L-shaped polygons with barriers.
Findings
Derived explicit volume formulas for eigenform loci.
Established asymptotic counting formulas for billiard paths.
Linked moduli space geometry to billiard dynamics.
Abstract
We compute the volumes of the eigenform loci in the moduli space of genus two Abelian differentials. From this, we obtain asymptotic formulas for counting closed billiards paths in certain L-shaped polygons with barriers.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Stochastic processes and statistical mechanics · Geometry and complex manifolds