The Relation of Spatial and Tensor Product of Arveson Systems --- The Random Set Point of View

We characterise the embedding of the spatial product of two Arveson systems into their tensor product using the random set technique. An important implication is that the spatial tensor product does not depend on the choice of the reference units, i.e. it is an intrinsic construction. There is a continuous range of examples coming from the zero sets of Bessel processes where the two products do not coincide. The lattice of all subsystems of the tensor product is analised in different cases. As a by-product, the Arveson systems coming from Bessel zeros prove to be primitive in the sense of \cite{JMP11a}

Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters

We investigate the breakdown of normal hyperbolicity of a manifold of equilibria of a flow. In contrast to classical bifurcation theory we assume the absence of any flow-invariant foliation at the singularity transverse to the manifold of equilibria. We call this setting bifurcation without parameters. In the present paper we provide a description of general systems with a manifold of equilibria of codimension one as a first step towards a classification of bifurcations without parameters. This is done by relating the problem to singularity theory of maps.Comment: corrected typos, minor clarifications in the formulation of the main theore