Invariant Measures for Set-Valued Dynamical Systems
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- by Walter Miller and Ethan Akin PDF
- Trans. Amer. Math. Soc. 351 (1999), 1203-1225 Request permission
Abstract:
A continuous map on a compact metric space, regarded as a dynamical system by iteration, admits invariant measures. For a closed relation on such a space, or, equivalently, an upper semicontinuous set-valued map, there are several concepts which extend this idea of invariance for a measure. We prove that four such are equivalent. In particular, such relation invariant measures arise as projections from shift invariant measures on the space of sample paths. There is a similarly close relationship between the ideas of chain recurrence for the set-valued system and for the shift on the sample path space.References
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Additional Information
- Walter Miller
- Affiliation: Department of Mathematics, Howard University, Washington, D.C. 20059
- Ethan Akin
- Affiliation: Department of Mathematics, The City College, New York, New York 10031
- MR Author ID: 24025
- Received by editor(s): June 14, 1996
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 1203-1225
- MSC (1991): Primary 54H20, 58F10, 34C35
- DOI: https://doi.org/10.1090/S0002-9947-99-02424-1
- MathSciNet review: 1637090