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# Compensation Functions for Shifts of Finite Type and a Phase Transition in the p-Dini Functions

 dc.contributor.author Antonioli, John dc.date.accessioned 2013-09-03T17:57:30Z dc.date.available 2013-09-03T17:57:30Z dc.date.copyright 2013 en_US dc.date.issued 2013-09-03 dc.identifier.uri http://hdl.handle.net/1828/4896 dc.description.abstract We study compensation functions for an infinite-to-one factor code $\pi : X \to Y$ where $X$ is a shift of finite type. The $p$-Dini condition is given as a way of measuring the smoothness of a continuous function, with $1$-Dini corresponding to functions with summable variation. Two types of compensation functions are defined in terms of this condition. Given a fully-supported invariant measure $\nu$ on $Y$, we show that the relative equilibrium states of a $1$-Dini function $f$ over $\nu$ are themselves fully supported, and have positive relative entropy. We then show that there exists a compensation function which is $p$-Dini for all $p > 1$ which has relative equilibrium states supported on a finite-to-one subfactor. en_US dc.language English eng dc.language.iso en en_US dc.subject compensation functions en_US dc.subject ergodic theory en_US dc.subject symbolic dynamics en_US dc.subject thermodynamic formalism en_US dc.title Compensation Functions for Shifts of Finite Type and a Phase Transition in the p-Dini Functions en_US dc.type Thesis en_US dc.contributor.supervisor Quas, Anthony dc.degree.department Dept. of Mathematics and Statistics en_US dc.degree.level Doctor of Philosophy Ph.D. en_US dc.rights.temp Available to the World Wide Web en_US dc.description.scholarlevel Graduate en_US dc.description.proquestcode 0405 en_US
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