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arXiv:1609.04943 [math.DS]AbstractReferencesReviewsResources

Convergence of Dynamics and the Perron-Frobenius Operator

Moritz Gerlach

Published 2016-09-16Version 1

We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent to setwise convergence of the underlying dynamic in the measure algebra. This situation is furthermore characterized by a uniform mixing-like property of the system.

Comments: 8 pages, 0 figures
Categories: math.DS, math.FA
Subjects: 37A05, 28D05, 37A25, 47A35
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