Some recent work in Fréchet geometry is briefly reviewed. In particular an earlier result on the structure of second tangent bundles in the finite dimensional case was extended to infinite dimensional Banach manifolds and Fréchet manifolds that could be represented as projective limits of Banach manifolds. This led to further results concerning the characterization of second tangent bundles and...

We study hypercyclicity of Toeplitz operators in the Hardy space H2(D) with symbols form R(z‾)+φ(z), where R is a rational function and φ∈H∞(D). relate this problem to cyclicity certain families functions for analytic give new sufficient conditions based on deep results B. Solomyak.

In this paper we introduce and study the notion of hypercyclicity for iterated function systems (IFS) operators. We prove that a linear IFS, implies sensitivity if an IFS is abelian, then also multi-sensitivity hence thick sensitivity. give some equivalent conditions as well weakly mixing