Advisor Feed
https://feeds.library.caltech.edu/people/Dunfield-N-M/advisor.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 06 Dec 2023 14:29:45 +0000Dynamics of Non-Classical Interval Exchanges
https://resolver.caltech.edu/CaltechTHESIS:04212010-181932550
Authors: Gadre, Vaibhav S.
Year: 2010
DOI: 10.7907/082X-F229
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.https://thesis.library.caltech.edu/id/eprint/5731