The Library
Thermodynamic formalism for symbolic dynamical systems
Tools
Kempton, Thomas (2011) Thermodynamic formalism for symbolic dynamical systems. PhD thesis, University of Warwick.
|
PDF
WRAP_THESIS_Kempton_2011.pdf - Submitted Version - Requires a PDF viewer. Download (669Kb) |
Official URL: http://webcat.warwick.ac.uk/record=b2521727~S15
Abstract
We derive results in the ergodic theory of symbolic dynamical systems.
Our first result concerns β-expansions of real numbers. We show that for a fixed
non-integer β > 1 and a fixed real number x ∈ [0, |β|/β-1], the number of words
(x1, ..., xn) that can be extended to β-expansions of x grows at least exponentially
in n.
Our second result concerns definitions of topological pressure for suspension
ows
over countable Markov shifts. Previously, topological pressure had been considered
for a restricted class of suspension
ows upon which the thermodynamic formalism
can be well understood using the base transformation. We consider a more general
class of suspension
ows and show the equivalence of several natural definitions of
topological pressure, including a definition analogous to that of Gurevich pressure
for a Markov shift.
Our third result concerns zero temperature limit laws for countable Markov shifts.
We show that for a uniformly locally constant potential f on a topologically mixing
countable Markov shift satisfying the big images and preimages property, the
equilibrium states μtf associated to the potential tf converge as t tends to infinity.
Finally we consider the image under a one-block factor map Π of a Gibbs measure μ
supported on a finite alphabet Markov shift. We give sufficient conditions on Π for
the image measure Π*(μ) to be a Gibbs measure and discuss regularity properties of
the potential associated to Π*(μ) in terms of the regularity of the potential associated
to μ.
Item Type: | Thesis (PhD) | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Ergodic theory, Dynamics, Markov processes | ||||
Official Date: | February 2011 | ||||
Dates: |
|
||||
Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Pollicott, Mark | ||||
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Extent: | vi, 130 leaves | ||||
Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year