For Axiom A diffeomorphisms the metric entropy of the SRB measure equals the sum of positive Lyapunov exponents, Birkhoff level sets have Hausdorff dimension given by the Legendre transform of pressure, coboundaries are characterized by periodic data, and the entropy production rate function obeys a
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Multifractal Analysis, Liv\v{s}ic Rigidity, and Fluctuation Theorems for Axiom A Diffeomorphisms: The Pesin Formula and the Gallavotti-Cohen Symmetry
For Axiom A diffeomorphisms the metric entropy of the SRB measure equals the sum of positive Lyapunov exponents, Birkhoff level sets have Hausdorff dimension given by the Legendre transform of pressure, coboundaries are characterized by periodic data, and the entropy production rate function obeys a