Optimization and majorization of invariant measures

Jenkinson, Oliver

doi:10.1090/S1079-6762-07-00170-9

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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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