Angle distortion theorems for starlike and spirallike functions with respect to a boundary point.
A flower structure of backward flow invariant domains for semigroups.
Dynamics of inequalities in geometric function theory.
Complex dynamical systems and the geometry of domains in Banach spaces
We consider semigroups of holomorphic self-mappings on domains in Hilbert and Banach spaces, and then develop a new dynamical approach to the study of geometric properties of biholomorphic mappings. We establish, for example, several flow invariance conditions and find parametric representations of semicomplete vector fields. In order to examine the asymptotic behavior of these semigroups, we use diverse tools such as hyperbolic metric theory and estimates of solutions of generalized differential...
On the Rogosinski radius for holomorphic mappings and some of its applications
The well known theorem of Rogosinski asserts that if the modulus of the sum of a power series is less than 1 in the open unit disk: , |z| < 1, then all its partial sums are less than 1 in the disk of radius 1/2: , |z| < 1/2, and this radius is sharp. We present a generalization of this theorem to holomorphic mappings of the open unit ball into an arbitrary convex domain. Other multidimensional analogs of Rogosinski’s theorem as well as some applications to dynamical systems are considered....
Parametric representations of semi-complete vector fields on the unit balls in and in Hilbert space
We present several characterizations and representations of semi-complete vector fields on the open unit balls in complex Euclidean and Hilbert spaces.
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