Proves structural stability, quasi-compactness of transfer operators with spectral gap, SRB measures as unique equilibrium states for the geometric potential, and Pesin entropy formula for Axiom A diffeomorphisms, yielding the Gibbs Equivalence Theorem via Markov partition coding.
Cambridge Studies in Advanced Mathematics151, Cambridge University Press, Cambridge
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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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Transfer Operators and SRB Measures for Axiom A Diffeomorphisms: Spectral Gap, Structural Stability, and the Gibbs Equivalence Theorem
Proves structural stability, quasi-compactness of transfer operators with spectral gap, SRB measures as unique equilibrium states for the geometric potential, and Pesin entropy formula for Axiom A diffeomorphisms, yielding the Gibbs Equivalence Theorem via Markov partition coding.
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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