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A note on operator semigroups associated to chaotic flows

Published online by Cambridge University Press:  11 February 2015

OLIVER BUTTERLEY
OLIVER BUTTERLEY*
Affiliation:
Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria email oliver.butterley@univie.ac.at
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Abstract

The transfer operator associated to a flow (continuous time dynamical system) is a one-parameter operator semigroup. We consider the operator-valued Laplace transform of this one-parameter semigroup. Estimates on the Laplace transform have been used in various settings in order to show the rate at which the flow mixes. Here we consider the case of exponential mixing and the case of rapid mixing (superpolynomial). We develop the operator theory framework amenable to this setting and show that the same estimates may be used to produce results, in terms of the operators, which go beyond the results for the rate of mixing.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 5 , August 2016 , pp. 1396 - 1408
Copyright
© Cambridge University Press, 2015 

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