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Decay of correlations in suspension semi-flows of angle-multiplying maps

Published online by Cambridge University Press:  01 February 2008

MASATO TSUJII
MASATO TSUJII*
Affiliation:
Department of Mathematics, Kyushu University, Fukuoka, 812-8581, Japan (email: [email protected])
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Abstract

We consider suspension semi-flows of angle-multiplying maps on the circle for Cr ceiling functions with r≥3. Under a Crgeneric condition on the ceiling function, we show that there exists a Hilbert space (anisotropic Sobolev space) contained in the L2 space such that the Perron–Frobenius operator for the time-t-map acts naturally on it and that the essential spectral radius of that action is bounded by the square root of the inverse of the minimum expansion rate. This leads to a precise description of decay of correlations. Furthermore, the Perron–Frobenius operator for the time-t-map is quasi-compact for a Cr open and dense set of ceiling functions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 1 , February 2008 , pp. 291 - 317
Copyright
Copyright © Cambridge University Press 2007

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