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Masur's log law and unique ergodicity

Banff International Research Station for Mathematical Innovation and Discovery

Teichmueller geodesics in moduli space are typically dense in this non-compact space. It is natural to ask how long it takes the typical geodesic to leave compact sets for the first time. In particular, we can exhaust moduli space by compact sets given by surfaces with no closed geodesics with length strictly less than c and ask how much time it takes a Teichmueller geodesic to leave such a set. Masur addressed this question by proving a logarithm law. Translation surfaces give Teichmueller geodesics and it is natural to ask if a Teichmuller geodesic satisfying Masur's logarithm law has that the vertical flow on the surface it arises from is uniquely ergodic. We show that it is for the flat systole but not necessarily for the extremal length systole (which coarsely gives distance in Teichmuller space). This is joint work with Rodrigo Trevino.

Mathematics; Dynamical systems and ergodic theory; Algebraic geometry; Dynamical systems

video/mp4

Author affiliation: University of Utah

2017-02-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59686

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/