Examples in Discrete Iteration of Arbitrary Intervals of Slopes

Given a compact interval [a, b]⊂[0, π], we construct a parabolic self-map of the upper half-plane whose set of slopes is [a, b]. The nature of this construction is completely discrete and explicit: we explicitly construct a self-map and we explicitly show in which way its orbits wander towards the D...

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Detalhes bibliográficos
Autores: Contreras Márquez, Manuel Domingo, Cruz Zamorano, Francisco José, Rodríguez Piazza, Luis
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/169508
Acesso em linha:https://hdl.handle.net/11441/169508
https://doi.org/10.1007/s12220-025-01934-4
Access Level:acceso abierto
Palavra-chave:Complex dynamics
Discrete iteration
The slope problem
Descrição
Resumo:Given a compact interval [a, b]⊂[0, π], we construct a parabolic self-map of the upper half-plane whose set of slopes is [a, b]. The nature of this construction is completely discrete and explicit: we explicitly construct a self-map and we explicitly show in which way its orbits wander towards the Denjoy–Wolff point. We also analyze some properties of the Herglotz measure corresponding to such example, which yield the regularity of such self-map in its Denjoy–Wolff point.