Citation
Gadre, Vaibhav S. (2010) Dynamics of Non-Classical Interval Exchanges. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/082X-F229. https://resolver.caltech.edu/CaltechTHESIS:04212010-181932550
Abstract
Train tracks with a single vertex are a generalization of interval exchange maps. Here, we consider non-classical interval exchanges: complete train tracks with a single vertex. These can be studied as a dynamical system by considering Rauzy induction in this context. This gives a refinement process on the parameter space similar to Kerckhoff's simplicial systems. We show that the refinement process gives an expansion that has a key dynamical property called uniform distortion. We use uniform distortion to prove normality of the expansion. Consequently, we prove an analog of Keane's conjecture: almost every non-classical interval exchange is uniquely ergodic. In the concluding chapter, we state an application of the main results of the thesis to a question about harmonic measures on the Thurston boundary of Teichmuller space coming from finitely supported random walks on the mapping class group.
Item Type: | Thesis (Dissertation (Ph.D.)) |
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Subject Keywords: | Interval exchange, Teichmuller space, Mapping class group |
Degree Grantor: | California Institute of Technology |
Division: | Physics, Mathematics and Astronomy |
Major Option: | Mathematics |
Thesis Availability: | Public (worldwide access) |
Research Advisor(s): |
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Thesis Committee: |
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Defense Date: | 2 April 2010 |
Record Number: | CaltechTHESIS:04212010-181932550 |
Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:04212010-181932550 |
DOI: | 10.7907/082X-F229 |
Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
ID Code: | 5731 |
Collection: | CaltechTHESIS |
Deposited By: | Vaibhav Gadre |
Deposited On: | 21 May 2010 15:48 |
Last Modified: | 08 Nov 2019 18:09 |
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