Geodesics on Flat Surfaces

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.

(25 pages, 5 figures) Based on the talk at ICM 2006 at Madrid; see Proceedings of the ICM, Madrid, Spain, 2006, EMS, 121-146 for the final version. For a more detailed survey see the paper "Flat Surfaces", arXiv.math.DS/0609392

References in corpus (2)

• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Multiple Saddle Connections on Flat Surfaces and Principal Boundary of the Moduli Spaces of Quadratic Differentials