, Volume 127, Issue 1, pp 253-277

MixingC rmaps of the interval without maximal measure

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

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.