Some results on stable manifolds (Q2745769)

The paper states some very general theorems on the existence of pseudo-stable and pseudo-unstable subspaces of Lipschitzian dynamical systems. In particular, these theorems imply classical results of Fenichel and Hirsch, Pugh and Shub on stable and unstable subspaces of compact invariant manifolds, the pseudo-(un)stable manifold theorem at a fixed point of Irwin, and Sternberg's theorem on smooth conjugacy of hyperbolic gems of maps or vector fields. The paper presents a sketch of proofs based on the Perron-Irwin approach via sequence spaces. The obtained results can be useful in the study of ``parabolic'' semiflows.