Israel Journal of Mathematics

, Volume 127, Issue 1, pp 253-277

First online:

MixingC rmaps of the interval without maximal measure

  • Sylvie RuetteAffiliated withInstitut de Mathématiques de Luminy, CNRS, case 907

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We construct aC rtransformation of the interval (or the torus) which is topologically mixing but has no invariant measure of maximal entropy. Whereas the assumption ofC ensures existence of maximal measures for an interval map, it shows we cannot weaken the smoothness assumption. We also compute the local entropy of the example.