Concave unimodal maps have no majorisation relations between their ergodic measures
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- by Jacob Steel PDF
- Proc. Amer. Math. Soc. 139 (2011), 2553-2558 Request permission
Abstract:
If $T$ is a concave unimodal map on the unit interval $[0,1]$ and $\{x:T^{n}(x) = 1 \text { for some } n\}$ is dense in $[0,1]$, we prove that all $T$-invariant ergodic Borel probability measures are mutually incomparable with respect to the partial order of majorisation. This contrasts sharply with the situation for other interval maps previously studied.References
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Additional Information
- Jacob Steel
- Affiliation: School of Mathematics, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
- Received by editor(s): March 18, 2010
- Received by editor(s) in revised form: June 4, 2010, and July 12, 2010
- Published electronically: December 30, 2010
- Communicated by: Bryna Kra
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 2553-2558
- MSC (2010): Primary 37E05; Secondary 37C40
- DOI: https://doi.org/10.1090/S0002-9939-2010-10705-0
- MathSciNet review: 2784820