4 papers
The Bergman and the growth numbers of domains and hyperbolic geometry
Manuel D. Contreras, Francisco J. Cruz-Zamorano, Luis Rodríguez-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 Rodríguez-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 complet…
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 th…
The Slope Problem in Discrete Iteration
Manuel D. Contreras, Francisco J. Cruz-Zamorano, Luis Rodríguez-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…