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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Noninvertible transformations admitting no absolutely continuous $ \sigma$-finite invariant measure


Authors: Jane M. Hawkins and Cesar E. Silva
Journal: Proc. Amer. Math. Soc. 111 (1991), 455-463
MSC: Primary 58F11; Secondary 28D05
MathSciNet review: 1045139
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Abstract: We study a family of $ n$-to-1 conservative ergodic endomorphisms which we will show to admit no $ \sigma $-finite absolutely continuous invariant measure. We exhibit recurrent measures for these transformations and study their ratio sets; the examples can be realized as $ {C^\infty }$ endomorphisms of the $ 2$-torus.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1045139-X
Article copyright: © Copyright 1991 American Mathematical Society