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.
Continuity of Lyapunov exponents forC r one- dimensional maps,arxiv:2510.18804, 2025
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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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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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Discontinuity of Lyapunov exponents vs Entropy for smooth surface diffeomorphisms
Presents a simplified argument for the continuity of Lyapunov exponents for measures near the maximal entropy measure in smooth surface diffeomorphisms.