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.
Grants:	European Commission 703269 Ministerio de Economía y Competitividad MDM-2014-0445 Ministerio de Economía y Competitividad MTM2017-86795-C3-3-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1374
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, 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.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
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

Postprint 26 p, 425.0 KB

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