8 papers
The Bergman and the growth numbers of domains and hyperbolic geometry
Manuel D. Contreras, Francisco J. Cruz-Zamorano, Luis RodrÃguez-Piazza
In this article we completely characterize the Bergman number of general domains. Namely, we prove that the Bergman number of a hyperbolic unbounded domain can be calculated in ter…
Examples in Discrete Iteration of Arbitrary Intervals of Slopes
Manuel D. Contreras, Francisco J. Cruz-Zamorano, Luis RodrÃguez-Piazza
Given a compact interval , we construct a parabolic self-map of the upper half-plane whose set of slopes is . The nature of this construction is comple…
Hardy Number of Koenigs Domains: Sharp Estimate
Manuel D. Contreras, Francisco J. Cruz-Zamorano, Maria Kourou +1
Let be a regular Koenigs domain in the complex plane . We prove that the Hardy number of is greater or equal to . That is, every holomorphic function in…
On the Hardy number of Koenigs domains
Manuel D. Contreras, Francisco J. Cruz-Zamorano, Maria Kourou +1
This work studies the Hardy number for the class of hyperbolic planar domains satisfying Abel's inclusion property, which are usually known as Koenigs domains. More explicitly, we…
The Slope Problem in Discrete Iteration
Manuel D. Contreras, Francisco J. Cruz-Zamorano, Luis RodrÃguez-Piazza
The slope problem in holomorphic dynamics in the unit disk goes back to Wolff in 1929. However, there have been several contributions to this problem in the last decade. In this ar…
Characterization of the hyperbolic step of parabolic functions
Manuel D. Contreras, Francisco J. Cruz-Zamorano, Luis RodrÃguez-Piazza
A classical problem in Complex Dynamics on hyperbolic domains is to characterize the hyperbolic step of parabolic functions. This topic has been studied by several authors, leading…