Partial entropies are upper semi-continuous for C^{1+α} diffeomorphisms when Lyapunov exponent sums are continuous, implying the same property at generic ergodic measures.
da Luz, Star flows with singularities of different indices,Preprint
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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.
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Continuity properties of partial entropy
Partial entropies are upper semi-continuous for C^{1+α} diffeomorphisms when Lyapunov exponent sums are continuous, implying the same property at generic ergodic measures.
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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.