C^∞ 3D flows with positive topological entropy admit only finitely many ergodic measures of maximal entropy, which are rapid mixing on a dense open set.
Bowen,Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Math., 470, Springer-Verlag, Berlin
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Thermodynamics formalism for singular flows
C^∞ 3D flows with positive topological entropy admit only finitely many ergodic measures of maximal entropy, which are rapid mixing on a dense open set.