6 papers
From discrete iteration in the unit disc to continuous semigroups of holomorphic functions
Argyrios Christodoulou, Konstantinos Zarvalis
The main goal of this article is to bring together the theories of holomorphic iteration in the unit disc and semigroups of holomorphic functions. We develop a technique that allow…
Extremal rate of convergence in continuous dynamics
Francisco J. Cruz-Zamorano, Konstantinos Zarvalis
This paper deals with semigroups of holomorphic self-maps of the upper half-plane that exhibit an extremal (i.e. the slowest possible) rate of convergence to their Denjoy--Wolff po…
Extremal rate of convergence in discrete hyperbolic and parabolic dynamics
Francisco J. Cruz-Zamorano, Konstantinos Zarvalis
This paper investigates the dynamical behaviour of holomorphic self-maps of the upper half-plane. More precisely, we focus on the hyperbolic and parabolic self-maps whose orbits ap…
Monotonicity properties of hyperbolic projections in holomorphic iteration
Argyrios Christodoulou, Konstantinos Zarvalis
We consider hyperbolic projections of orbits of holomorphic self-maps of the unit disc, onto curves landing on the unit circle with a given angle. We show that under certain, neces…
On the rates of convergence of orbits in semigroups of holomorphic functions
Dimitrios Betsakos, Francisco J. Cruz-Zamorano, Konstantinos Zarvalis
Let be a continuous semigroup of holomorphic self-maps of the unit disk with Denjoy-Wolff point . We study the rate of convergence o…
Semigroups of holomorphic functions; rectifiability and Lipschitz properties of the orbits
Dimitrios Betsakos, Konstantinos Zarvalis
Let be a semigroup of holomorphic functions in the unit disk. We prove that all its orbits are rectifiable and that its forward orbits are Lipschitz curves. Moreover, we fi…