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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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 |
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510 QA Mathematics |
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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 |
_version_ |
1718142561338523648 |