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A bound on the number of rationally invisible repelling orbits
Benini, Anna Miriam (Università di Parma. Dipartimento di Scienze Matematiche Fisiche e Informatiche (Italy))
Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)

Date: 2020
Abstract: We consider entire transcendental maps with bounded set of singular values such that periodic rays exist and land. For such maps, we prove a refined version of the Fatou-Shishikura inequality which takes into account rationally invisible periodic orbits, that is, repelling cycles which are not landing points of any periodic ray. More precisely, if there are q<∞ singular orbits, then the sum of the number of attracting, parabolic, Siegel, Cremer or rationally invisible orbits is bounded above by q. In particular, there are at most q rationally invisible repelling periodic orbits. The techniques presented here also apply to the more general setting in which the function is allowed to have infinitely many singular values.
Note: Número d'acord de subvenció EC/H2020/703269
Note: Número d'acord de subvenció MINECO/MDM-2014-0445
Note: Número d'acord de subvenció MINECO/MTM2017-86795-C3-3-P
Note: Número d'acord de subvenció AGAUR/2017/SGR-1374
Rights: Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. Creative Commons
Language: Anglès
Document: article ; recerca ; acceptedVersion
Subject: Transcendental maps ; Fatou-Shishikura inequality ; Holomorphic dynamics ; Accessibility
Published in: Advances in Mathematics, Vol. 370 (August 2020) , art. 107214, ISSN 1090-2082

DOI: 10.1016/j.aim.2020.107214


Available from: 2022-08-31
Postprint

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2020-07-15, last modified 2020-08-01



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