Floquet operators with singular spectrum. III
Cet article est consacré à l’étude d’une large classe de flots d’Anosov sur les variétés graphées. Nous établissons un résultat général à propos des plongements de variétés de Seifert dans les variétés de dimension 3 admettant un flot d’Anosov produit, généralisant ainsi un résultat de E. Ghys. Nous montrons que, à isotopie près, la restriction du feuilletage unidimensionnel défini par le flot à l’image de ce plongement est topologiquement conjugué à un morceau de flot géodésique privé d’un nombre...
We describe the extension of the multiplication on a not-necessarily-discrete topological monoid to its flow compactification. We offer two applications. The first is a nondiscrete version of Hindman’s Theorem, and the second is a characterization of the projective minimal and elementary flows in terms of idempotents of the flow compactification of the monoid.
We describe necessary and sufficient conditions for a fixed point free planar homeomorphism that preserves the standard Reeb foliation to embed in a planar flow that leaves the foliation invariant.
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...
We consider a fixed point free homeomorphism of the closed band which leaves each leaf of a Reeb foliation on invariant. Assuming is the time one of various topological flows, we compare the restriction of the flows on the boundary.