Smoothness of stable holonomies inside center-stable manifolds and the C2 hypothesis in Pugh-Shub and Ledrappier-Young theory
Abstract
Under a suitable bunching condition, we establish that stable holonomies inside center-stable manifolds for C1+β diffeomorphisms are uniformly bi-Lipschitz and in fact C1+H\"older. This verifies that the Pugh-Shub theory for ergodicity holds for suitably center-bunched, C1+β, essentially accessible, partially hyperbolic diffeomorphism and verifies that the Ledrappier-Young entropy formulas hold for C1+β diffeomorphisms of compact manifolds.
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