Geodesics on Flat Surfaces
Anton Zorich
TL;DR
This survey explores Teichmuller dynamics and their application to understanding the asymptotic behavior of geodesics on flat surfaces, including counting closed geodesics and saddle connections.
Contribution
It synthesizes joint research on Teichmuller dynamics, providing insights into the topology and geodesic counting on flat surfaces.
Findings
Asymptotic topology of generic geodesics analyzed
Methods for counting closed geodesics developed
Connections to Teichmuller dynamics established
Abstract
This short survey illustrates the ideas of Teichmuller dynamics. As a model application we consider the asymptotic topology of generic geodesics on a "flat" surface and count closed geodesics and saddle connections. This survey is based on the joint papers with A.Eskin and H.Masur and with M.Kontsevich.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · Geometry and complex manifolds