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.

Lecture #12590

Need help? Visit our help pages at http://www.msri.org/communications/vmath/hints

Supplements

Right click on the link and "Save As..." to save to your local computer.

• 12590.pdf (2.2 MB)

Left click on thumbnail to see a larger image.

Streaming Video

This is a high quality streaming video encoded with MPEG-4 and with 640x480 resolution.

Windows and Mac users, QuickTime 6.5 or later required
Linux users, please see our Linux Help Page on how to view our streaming videos

Follow this link to --- Watch the Video Now Via Streaming Video ---

Download QuickTime File

You can download the QuickTime file here. Right click on the link and "Save As..." to save to your local computer.

• 12590-12590-QuickTime.mov (329 MB)

Create a DVD

You can download the video and audio files here. Please note that you need both files to create a DVD. Right click on the link and "Save As..." to save to your local computer. You can find instructions on how to create a DVD on our help page at http://www.msri.org/communications/vmath/author

• 12590-12590-DVD PCM Audio.aiff (675 MB - Audio Only)
• 12590-12590-MPEG-2 120min High Quality Encode.m2v (1540 MB - Video Only)

Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture.

If you would like to purchase a copy of this video for $15+shipping, please Click Here!

See more of our Streaming Videos on our main VMath - Streaming Video page.