Dynamical determinants and their applications

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...

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Main Author: Felton, Philip
Published: University of Warwick 2012
Subjects:
510
Online Access:http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.572930
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spelling ndltd-bl.uk-oai-ethos.bl.uk-5729302015-12-03T03:42:55ZDynamical determinants and their applicationsFelton, Philip2012This 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.510QA MathematicsUniversity of Warwickhttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.572930http://wrap.warwick.ac.uk/54674/Electronic Thesis or Dissertation
collection NDLTD
sources NDLTD
topic 510
QA Mathematics
spellingShingle 510
QA Mathematics
Felton, Philip
Dynamical determinants and their applications
description 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.
author Felton, Philip
author_facet Felton, Philip
author_sort Felton, Philip
title Dynamical determinants and their applications
title_short Dynamical determinants and their applications
title_full Dynamical determinants and their applications
title_fullStr Dynamical determinants and their applications
title_full_unstemmed Dynamical determinants and their applications
title_sort dynamical determinants and their applications
publisher University of Warwick
publishDate 2012
url http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.572930
work_keys_str_mv AT feltonphilip dynamicaldeterminantsandtheirapplications
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