Dynamical Systems
Entropy and maximizing measures of generic continuous functions
Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 199-201.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.01.006
Brémont, Julien 1

1 Laboratoire d'analyse et de mathématiques appliquées, université Paris XII, faculté des sciences et technologies, 61, avenue du Général-de-Gaulle, 94010 Créteil cedex, France
@article{CRMATH_2008__346_3-4_199_0,
     author = {Br\'emont, Julien},
     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},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2008.01.006/}
}
TY  - JOUR
AU  - Brémont, Julien
TI  - Entropy and maximizing measures of generic continuous functions
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 199
EP  - 201
VL  - 346
IS  - 3-4
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2008.01.006/
DO  - 10.1016/j.crma.2008.01.006
LA  - en
ID  - CRMATH_2008__346_3-4_199_0
ER  - 
%0 Journal Article
%A Brémont, Julien
%T Entropy and maximizing measures of generic continuous functions
%J Comptes Rendus. Mathématique
%D 2008
%P 199-201
%V 346
%N 3-4
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2008.01.006/
%R 10.1016/j.crma.2008.01.006
%G en
%F CRMATH_2008__346_3-4_199_0
Brémont, Julien. 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. http://www.numdam.org/articles/10.1016/j.crma.2008.01.006/

[1] Bousch, T. La condition de Walters, Ann. Sci. ENS, Volume 34 (2001), pp. 287-311

[2] Bousch, T.; Jenkinson, O. Cohomology classes of dynamically non-negative Ck functions, Invent. Math., Volume 148 (2002), pp. 207-217

[3] Brémont, J. 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] Denker, M.; Grillenberger, C.; Sigmund, K. Ergodic Theory on Compact Spaces, Lecture Notes in Mathematics, vol. 527, Springer-Verlag, Berlin, 1976

[6] Jenkinson, O. Ergodic optimization, Discrete Contin. Dynam. Systems, Volume 15 (2006), pp. 197-224

[7] O. Jenkinson, I. Morris, Lyapunov optimizing measures for C1 expanding maps of the circle, Preprint, 2007

[8] Pollicott, M.; Sharp, R. Livsic theorems, maximizing measures and the stable norm, Dynam. Systems, Volume 19 (2004), pp. 75-88

[9] Ruelle, D. Thermodynamic Formalism, Cambridge University Press, Cambridge, 2004

Cited by Sources: