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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An optimized upper bound on the loss of upper semi-continuity of metric entropy for C^r diffeomorphisms, shown to be sharp via Buzzi's examples.
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.
citing papers explorer
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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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On the loss of upper semi-continuity of metric entropy for $C^{r}$ diffeomorphisms
An optimized upper bound on the loss of upper semi-continuity of metric entropy for C^r diffeomorphisms, shown to be sharp via Buzzi's examples.
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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.