Fischer, Torsten and Rugh, Hans Henrik (2000) Transfer operators for coupled analytic maps. Ergodic Theory and Dynamical Systems, Vol.20 (No.1). pp. 109-143. doi:10.1017/S0143385700000079 ISSN 0143-3857.

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Abstract

We consider analytically coupled circle maps (uniformly expanding and analytic) on the ${\mathbb Z}^d$-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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Banach spaces, Mappings (Mathematics), Circle, Calculus of residues, Transfer operators
Journal or Publication Title:	Ergodic Theory and Dynamical Systems
Publisher:	Cambridge University Press
ISSN:	0143-3857
Official Date:	February 2000
Dates:	Date Event February 2000 Published
Volume:	Vol.20
Number:	No.1
Page Range:	pp. 109-143
DOI:	10.1017/S0143385700000079
Status:	Peer Reviewed
Access rights to Published version:	Open Access (Creative Commons)
Funder:	Fifth Framework Programme (European Commission) (FP5)
Grant number:	ERBFMBICT-961157 (FFP)

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