Feuilletages Proches d'une Fibration. / C. Bonatti.
Flow invariance for perturbed nonlinear evolution equations.
Flows near compact invariant sets. Part I
It is proved that near a compact, invariant, proper subset of a C⁰ flow on a locally compact, connected metric space, at least one, out of twenty eight relevant dynamical phenomena, will necessarily occur. Theorem 1 shows that the connectedness of the phase space implies the existence of a considerably deeper classification of topological flow behaviour in the vicinity of compact invariant sets than that described in the classical theorems of Ura-Kimura and Bhatia. The proposed classification brings...