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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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