Ergodic optimization is the study of which ergodic measures maximize the integral of a particular function. For sufficiently regular functions, e.g. Lipschitz/Holder continuous functions, it is conjectured that the set of functions optimized by measures supported on a periodic orbit is dense. Yuan and Hunt made great progress towards showing this for Lipschitz functions. This thesis presents clear proofs of Yuan and Hunt’s theorems in the case of the Shift as well as introducing a subset of Lipschitz functions, the super-continuous functions, where the set of functions optimized by measures supported on a periodic orbit is open and dense.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/2922 |
| Date | 06 August 2010 |
| Creators | Siefken, Jason |
| Contributors | Quas, Anthony |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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