Flow around a slender circular cylinder: a case study on distributed Hopf bifurcation.
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.
We obtain a classification of codimension one holomorphic foliations on with degenerate Gauss maps.