Characterization of topologically transitive attractors for analytic plane flows

We give necessary conditions for a set to be topologically transitive attractor of an analytic plane flow using topological characterization of ?-limit sets and the concept of upper semi-continuity of multi valued maps.

Topological equivalence of finitely determined real analytic plane-to-plane map germs

Generic smooth map germs $({\mathsf R}^2,0)\to ({\mathsf R}^2,0)$ are topologically equivalent to cones of mappings $S^1\to S^1$. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determined real analytic map germs $({\mathsf R}^2,0)\to ({\mathsf R}^2,0)$.

Global attractors of analytic plane flows

In this paper the global attractors of analytic and polynomial plane flows are characterized up to homeomorphisms. Following on from previous results for continuous and differentiable dynamical systems, our theorem completes the characterization of the global attractors of plane flows.

Operators acting on certain Banach spaces of analytic functions

Let𝒳be reflexive Banach space of functions analytic plane domainΩsuch that for everyλinΩthe functional of evaluation atλis bounded. Assume further that𝒳contains the constants andMzmultiplication by the independent variablez, is bounded operator on𝒳. We give sufficient conditions forMzto be reflexive. In particular, we prove that the operatorsMzonEP(Ω)and certainHaP(β)reflexive. We also prove that the algebra of multiplication operators on Bergman spaces is reflexive, giving simpler proof of result of Eschmeier.

On the semigroup of an ordinary multiple point

In this paper we define the semigroup of an ordinary multiple point of an analytic plane curve f. This semigroup on tuples of integers is completely characterised in terms of the order of f, that is the number of distinct tangent directions to f at that point.