A natural family of equilibrium measures for the billiard flow, including the MME
speaker: Jérôme Carrand (Sorbonne Université)abstract: An equilibrium measure is a measure maximizing a certain quantity depending on the entropy and a potential. We give two conditions for a given Hölder potential to be associated with a unique equilibrium measure for the collision map. To construct these measures, we use maximal eigenvectors associated to transfer operators acting on an anisotropic Banach space. The particular form of these measures allows us to show that they are of full support and Bernoulli. With V. Baladi and M. Demers, on the basis of the conditions introduced previously, we obtain the existence, uniqueness and Bernoullianity of the maximal entropy measure for the billiard flow, assuming only the finite horizon and a weak condition (which we also believe to be generic).
timetable:
Thu 15 Dec, 11:30 - 12:30, Aula Dini
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