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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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Amenable relations for endomorphisms
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by J. M. Hawkins PDF
Trans. Amer. Math. Soc. 343 (1994), 169-191 Request permission

Abstract:

We give necessary and sufficient conditions for an endomorphism to admit an equivalent invariant $\sigma$-finite measure in terms of a generalized Perron-Frobenius operator. The assumptions are that the endomorphism is nonsingular (preserves sets of measure zero), conservative, and finite-to-1. We study two orbit equivalence relations associated to an endomorphism, and their connections to nonsingularity, ergodicity, and exactness. We also discuss Radon-Nikodym derivative cocycles for the relations and the endomorphism, and relate these to the Jacobian of the endomorphism.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 343 (1994), 169-191
  • MSC: Primary 28D99
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1179396-3
  • MathSciNet review: 1179396