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Mathematics  2005 

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

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Abstract:

We consider suspension semi-flows of angle-multiplying maps on the circle. Under a $C^r$generic condition on the ceiling function, we show that there exists an anisotropic Sobolev space contained in the $L^2$ space such that the Perron-Frobenius operator for the time-$t$-map acts 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 on decay of correlations and extends the result of M. Pollicott.

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