Noninvertible transformations admitting no absolutely continuous $\sigma$-finite invariant measure
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- by Jane M. Hawkins and Cesar E. Silva PDF
- Proc. Amer. Math. Soc. 111 (1991), 455-463 Request permission
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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 455-463
- MSC: Primary 58F11; Secondary 28D05
- DOI: https://doi.org/10.1090/S0002-9939-1991-1045139-X
- MathSciNet review: 1045139