In the natural context of ergodic optimization, we provide a short proof of the assertion that the maximizing measure of a generic continuous function has zero entropy.
Dans le cadre usuel de l'étude des mesures maximisantes, nous donnons une preuve courte du fait que la mesure maximisante d'une fonction continue générique est d'entropie nulle.
Accepted:
Published online:
Julien Brémont 1
@article{CRMATH_2008__346_3-4_199_0, author = {Julien Br\'emont}, title = {Entropy and maximizing measures of generic continuous functions}, journal = {Comptes Rendus. Math\'ematique}, pages = {199--201}, publisher = {Elsevier}, volume = {346}, number = {3-4}, year = {2008}, doi = {10.1016/j.crma.2008.01.006}, language = {en}, }
Julien Brémont. Entropy and maximizing measures of generic continuous functions. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 199-201. doi : 10.1016/j.crma.2008.01.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.01.006/
[1] La condition de Walters, Ann. Sci. ENS, Volume 34 (2001), pp. 287-311
[2] Cohomology classes of dynamically non-negative functions, Invent. Math., Volume 148 (2002), pp. 207-217
[3] Finite flowers and maximizing measures for generic Lipschitz functions on the circle, Nonlinearity, Volume 19 (2006), pp. 813-828
[4] J.-P. Conze, Y. Guivarc'h, Croissance des sommes ergodiques et principe variationnel, Tech. report, Université de Rennes 1, 1990
[5] Ergodic Theory on Compact Spaces, Lecture Notes in Mathematics, vol. 527, Springer-Verlag, Berlin, 1976
[6] Ergodic optimization, Discrete Contin. Dynam. Systems, Volume 15 (2006), pp. 197-224
[7] O. Jenkinson, I. Morris, Lyapunov optimizing measures for expanding maps of the circle, Preprint, 2007
[8] Livsic theorems, maximizing measures and the stable norm, Dynam. Systems, Volume 19 (2004), pp. 75-88
[9] Thermodynamic Formalism, Cambridge University Press, Cambridge, 2004
Cited by Sources:
Comments - Policy