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Transfer operators for deterministic and stochastic coupled map lattices.
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Fischer, Torsten (1998) Transfer operators for deterministic and stochastic coupled map lattices. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3065801~S15
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.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Transfer operators, Coupled map lattices, Banach spaces | ||||
| Official Date: | August 1998 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Rugh, Hans Henrik | ||||
| Sponsors: | European Commission. Training and Mobility of Researchers Programme | ||||
| Format of File: | |||||
| Extent: | iv, 119 leaves : illustrations | ||||
| Language: | eng |
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