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Felton, Philip (2012) Dynamical determinants and their applications. PhD thesis, University of Warwick.
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WRAP_THESIS_Felton_2012.pdf - Submitted Version Download (1984Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b2623462~S1
Abstract
This thesis is concerned with situations where we can define trace-class transfer oper-
ators, and extract useful information from their determinants.
The first topic is on Lyapunov exponents of random products of matrices. We obtain
a new expression for the Lyapunov exponent of a continuous family of matrices, and a
slightly different version of existing work for the discrete case.
The second topic explores possibilities of using similar theory to approximate eigen-
functions of the Laplacian for surfaces of constant negative curvature.
The third topic gives a variety of approximations of Mahler measures, which occur in
many different areas of mathematics, by manipulating the integrals into a form that can
be numerically integrated using work of Pollicott and Jenkinson.
The final topic of the thesis works out the details of earlier ideas of Pollicott, to give
a method for the numerical approximation of entropy rates of hidden Markov processes.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Determinants, Lyapunov exponents, Matrices, Eigenfunctions, Laplacian matrices, Markov processes | ||||
Official Date: | July 2012 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Pollicott, Mark | ||||
Extent: | vi, 128 leaves. | ||||
Language: | eng |
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