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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Concave unimodal maps have no majorisation relations between their ergodic measures


Author: Jacob Steel
Journal: Proc. Amer. Math. Soc. 139 (2011), 2553-2558
MSC (2010): Primary 37E05; Secondary 37C40
Published electronically: December 30, 2010
MathSciNet review: 2784820
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Abstract: If $ T$ is a concave unimodal map on the unit interval $ [0,1]$ and $ \{x:T^{n}(x) = 1$    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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10705-0
PII: S 0002-9939(2010)10705-0
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
Article copyright: © Copyright 2010 American Mathematical Society