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.
Upper semi-continuity of metric entropy for
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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.
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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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Chaos on surfaces and beyond: a new notion of dynamical hyperbolicity
Strong positive recurrence is a property satisfied by all smooth surface diffeomorphisms with positive entropy that guarantees exponential mixing and limit theorems.
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Entropy formula for surface diffeomorphisms
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.
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