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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Autores: Contreras Márquez, Manuel Domingo, Cruz Zamorano, Francisco José, Rodríguez Piazza, Luis
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/169508
Acceso en línea:https://hdl.handle.net/11441/169508
https://doi.org/10.1007/s12220-025-01934-4
Access Level:acceso abierto
Palabra clave:Complex dynamics
Discrete iteration
The slope problem
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spelling Examples in Discrete Iteration of Arbitrary Intervals of SlopesContreras Márquez, Manuel DomingoCruz Zamorano, Francisco JoséRodríguez Piazza, LuisComplex dynamicsDiscrete iterationThe slope problemGiven 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.SpringerMatemática Aplicada IIAnálisis Matemático2025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/169508https://doi.org/10.1007/s12220-025-01934-4reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésThe Journal of Geometric Analysis, 35, 99.https://link.springer.com/article/10.1007/s12220-025-01934-4info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1695082026-06-17T12:51:07Z
dc.title.none.fl_str_mv Examples in Discrete Iteration of Arbitrary Intervals of Slopes
title Examples in Discrete Iteration of Arbitrary Intervals of Slopes
spellingShingle Examples in Discrete Iteration of Arbitrary Intervals of Slopes
Contreras Márquez, Manuel Domingo
Complex dynamics
Discrete iteration
The slope problem
title_short Examples in Discrete Iteration of Arbitrary Intervals of Slopes
title_full Examples in Discrete Iteration of Arbitrary Intervals of Slopes
title_fullStr Examples in Discrete Iteration of Arbitrary Intervals of Slopes
title_full_unstemmed Examples in Discrete Iteration of Arbitrary Intervals of Slopes
title_sort Examples in Discrete Iteration of Arbitrary Intervals of Slopes
dc.creator.none.fl_str_mv Contreras Márquez, Manuel Domingo
Cruz Zamorano, Francisco José
Rodríguez Piazza, Luis
author Contreras Márquez, Manuel Domingo
author_facet Contreras Márquez, Manuel Domingo
Cruz Zamorano, Francisco José
Rodríguez Piazza, Luis
author_role author
author2 Cruz Zamorano, Francisco José
Rodríguez Piazza, Luis
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada II
Análisis Matemático
dc.subject.none.fl_str_mv Complex dynamics
Discrete iteration
The slope problem
topic Complex dynamics
Discrete iteration
The slope problem
description 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.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/169508
https://doi.org/10.1007/s12220-025-01934-4
url https://hdl.handle.net/11441/169508
https://doi.org/10.1007/s12220-025-01934-4
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv The Journal of Geometric Analysis, 35, 99.
https://link.springer.com/article/10.1007/s12220-025-01934-4
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.228081

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