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.
Zang, Measures of maximal entropy forC ∞ three-dimensional flows
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Strong positive recurrence is a property satisfied by all smooth surface diffeomorphisms with positive entropy that guarantees exponential mixing and limit theorems.
For C^r surface diffeomorphisms with h_top(f) ≥ λ⁺(f)/r, h_top(f) equals lim (1/n) log ∫_M ||Df^n_x|| dx.
Presents a simplified argument for the continuity of Lyapunov exponents for measures near the maximal entropy measure in smooth surface diffeomorphisms.
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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.