Convergence of dynamics and the Perron–Frobenius operator
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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 uniform mixing-like properties of the system.
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