Fixed points of two-sided fractional matrix transformations.
The aim of this work is to study global -webs with vanishing curvature. We wish to investigate degree foliations for which their dual web is flat. The main ingredient is the Legendre transform, which is an avatar of classical projective duality in the realm of differential equations. We find a characterization of degree foliations whose Legendre transform are webs with zero curvature.
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...