Transfer operators for coupled analytic maps
2000 ◽
Vol 20
(1)
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pp. 109-143
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Keyword(s):
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.
2007 ◽
Vol 17
(05)
◽
pp. 1673-1685
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2020 ◽
Vol 37
(4)
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pp. 1367-1399
2013 ◽
Vol 8
(11)
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pp. 349-359
2001 ◽
Vol 432
◽
pp. 167-200
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2011 ◽
Vol 53
(3)
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pp. 443-449
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