Problem 34

If $\mu $ is an equilibrium state for some continuous $g$ on $\Sigma _N^+$, is $h_\mu >0$?

Comments

  • Ledrappier (2016-11-14 13:50:14 -0800 -0800):

    No, every ergodic measure is the equilibrium state of some continuous function. Abstract convexity properties (cf. [israel1984some] ).