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Topics in Teichmuller Theory and Kleinian Groups |
| November 12, 2007 to November 16, 2007 |
| Organized By: Jeff Brock, Ken Bromberg, Richard Canary, Howard Masur, Alan Reid, Maryam Mirzakhani, and John Smillie |
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| Parent Programs: |
| Teichmuller Theory and Kleinian Groups |
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| Return to Workshop Description |
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Ergodic properties of surface flows
Monday November 12, 2007
11:00AM - 12:00PM
Speakers:
Corinna Ulcigrai
Abstract:
Teichmuller dynamics is known to be a key tool to understand the ergodic
properties of flows on translation surfaces and of interval exhange
transformations (IETs), one dimensional maps which appear as cross sections
of such flows. In this talk we will briefly introduce the Rauzy-Veech
algorithm (which is a discrete version of the Teichmuller flow on abelian
differentials) and present two results in which Teichmuller dynamics is
used.
We consider a different class of area-preserving flows on surfaces, flows
given by multi-valued Hamiltonians. Such flows can be described as
suspension flows over IETs with logarithmic singularities. We show that in
the asymmetric case such flows are typically mixing and that in the
symmetric case they are typically weakly mixing. Time permitting, we will
present also a limit theorem for denominators of the continued fraction
which exploits mixing of the Teichmuller flow. The latter is a join work
with Sinai.
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