Absolute continuity of stable foliations for systems on Banach spaces
The main result of the paper is the absolute continuity of stable foliations for \(C^{1, \alpha}\) maps of Banach spaces, satisfying a globally defined infinitesimal invariant cones condition. The authors also prove existence and regularity for center and stable manifolds under technical assumptions, needed for the main theorem. The results can be applied to infinite-dimensional dynamical systems generated by ordinary, partial or functional differential equations. Some examples of differential equations are provided. The proofs are based on graph transform methods.
scientific article; zbMATH DE number 6109883