Convergence of Dynamics and the Perron-Frobenius Operator

Autoren: Moritz Gerlach (2018)

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.

Zeitschrift:
Israel Journal of Mathematics
Seiten:
451–463
Band:
225(1)

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