Optimization and majorization of invariant measures

Jenkinson, Oliver¹

¹School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK

Electronic research announcements of the American Mathematical Society, Tome 13 (2007), pp. 1-12

Résumé

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.

Détail

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

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