Frobenius-Perron operators and approximation of invariant measures for set-valued dynamical systems Article Received: 07 October 1993 Revised: 27 December 1994 DOI:
Cite this article as: Miller, W.M. Set-Valued Anal (1995) 3: 181. doi:10.1007/BF01038599 Abstract
A set-valued dynamical system
F on a Borel space X induces a set-valued operator F on M( X) — the set of probability measures on X. We define a representation of F, each of which induces an explicitly defined selection of F; and use this to extend the notions of invariant measure and Frobenius-Perron operators to set-valued maps. We also extend a method of S. Ulam to Markov finite approximations of invariant measures to the set-valued case and show how this leads to the approximation of T-invariant measures for transformations τ, where T corresponds to the closure of the graph of τ. Mathematics Subject Classifications (1991) Primary: 58F11 Secondary: 54C60, 60J05 Key words Frobenius-Perron operators invariant measures ergodic theory set-valued dynamical systems relations random perturbations References
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© Kluwer Academic Publishers 1995