Smoothness of stable holonomies inside center-stable manifolds and the hypothesis in Pugh-Shub and Ledrappier-Young theory
arXiv:1608.05886
Abstract
Under a suitable bunching condition, we establish that stable holonomies inside center-stable manifolds for diffeomorphisms are uniformly bi-Lipschitz and in fact . This verifies that the Pugh-Shub theory for ergodicity holds for suitably center-bunched, , essentially accessible, partially hyperbolic diffeomorphism and verifies that the Ledrappier-Young entropy formulas hold for diffeomorphisms of compact manifolds.