Optimization and majorization of invariant measures
Author:
Oliver Jenkinson
Journal:
Electron. Res. Announc. Amer. Math. Soc. 13 (2007), 1-12
MSC (2000):
Primary 37A05, 37D20, 37E05; Secondary 37B10, 37E45, 37F15, 46A55
DOI:
https://doi.org/10.1090/S1079-6762-07-00170-9
Published electronically:
February 5, 2007
MathSciNet review:
2285761
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Abstract: The set of $\times 2$-invariant measures can be equipped with the partial order of majorization, describing relative dispersion. The minimal elements for this order are precisely the Sturmian measures of Morse and Hedlund. This yields new characterisations of Sturmian measures, and has applications to the ergodic optimization of convex functions.
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bouschjenkinson T. Bousch & O. Jenkinson, Cohomology classes of dynamically non-negative $C^k$ functions, Invent. Math., 148 (2002), 207–217.
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Additional Information
Oliver Jenkinson
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK
MR Author ID:
657004
Email:
omj@maths.qmul.ac.uk
Keywords:
Invariant measures,
majorization,
dilation,
ergodic optimization
Received by editor(s):
September 15, 2006
Published electronically:
February 5, 2007
Additional Notes:
The author was supported by an EPSRC Advanced Research Fellowship
Communicated by:
Klaus Schmidt
Article copyright:
© Copyright 2007
American Mathematical Society