Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302684
Title: Transfer operators for deterministic and stochastic coupled map lattices
Author: Fischer, Torsten
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1998
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Abstract:
In Chapter One we consider analytically coupled circle maps (uniformly expanding and analytic) on the Zd-lattice with exponentially decaying interaction. We introduce Banach spaces for the infinite-dimensional system that include measures whose finite-dimensional marginals have analytic, exponentially bounded densities. Using residue calculus and 'cluster expansion'-like techniques we define transfer operators on these Banach spaces. We get a unique (in the considered Banach spaces) probability measure that exhibits exponential decay of correlations. In Chapter Two we consider on M = (S1)Zd a family of continuous local updatings, of finite range type or Lipschitz-continuous in all coordinates with summable Lipschitz-constants. We show that the infinite-dimensional dynamical system with independent identically Poisson-distributed times for the individual updatings is well-defined. In the setting of analytically coupled uniformly expanding, analytic circle maps with weak, exponentially decaying interaction, we define transfer operators for the infinite-dimensional system, acting on Banach-spaces that include measures whose finite-dimensional marginals have analytic, exponentially bounded densities. We prove existence and uniqueness (in the considered Banach space) of a probability measure and its exponential decay of correlations.
Supervisor: Not available Sponsor: European Commission (Training and Mobility of Researchers Programme)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.302684  DOI: Not available
Keywords: QA Mathematics Mathematics
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