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arXiv · 1609.04943

Convergence of Dynamics and the Perron-Frobenius Operator

Moritz Gerlach
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Abstract

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.

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Moritz Gerlach. 2017-03-29. Convergence of Dynamics and the Perron-Frobenius Operator. https://arxiv.org/abs/1609.04943

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