Smoothness of stable holonomies inside center-stable manifolds
Aaron Brown
Abstract
Abstract Under a suitable bunching condition, we establish that stable holonomies inside center-stable manifolds for $C^{1+\beta }$ diffeomorphisms are uniformly bi-Lipschitz and, in fact, $C^{1+\mathrm {H}\ddot{\rm o}\mathrm {lder}}$ . This verifies the ergodicity of suitably center-bunched, essentially accessible, partially hyperbolic $C^{1+\beta }$ diffeomorphisms and verifies that the Ledrappier–Young entropy formula holds for $C^{1+\beta }$ diffeomorphisms of compact manifolds.
Topics & Concepts
MathematicsCenter (category theory)Lipschitz continuitySmoothnessPure mathematicsDiffeomorphismMathematical analysisManifold (fluid mechanics)ErgodicityCombinatoricsCrystallographyMechanical engineeringStatisticsEngineeringChemistryMathematical Dynamics and FractalsQuantum chaos and dynamical systemsAdvanced Differential Equations and Dynamical Systems