Singular values and non-repelling cycles for entire transcendental maps
Benini, Anna Miriam (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)

Date:	2020
Abstract:	Let f be a map with bounded set of singular values for which periodic dynamic rays exist and land. We prove that each non-repelling cycle is associated to a singular orbit which cannot accumulate on any other non-repelling cycle. When f has finitely many singular values this implies a refinement of the Fatou-Shishikura inequality. Our approach is combinatorial in the spirit of the approach used by [Kiw00], [BCL+16] for polynomials.
Grants:	European Commission 703269 Ministerio de Economía y Competitividad MTM2014-52209-C2-2-P Ministerio de Economía y Competitividad MDM-2014-0445
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió sotmesa a revisió
Published in:	Indiana University mathematics journal, Vol. 69, Issue 5 (2020) , p. 1543-1558, ISSN 0022-2518

DOI: 10.1512/iumj.2020.69.8000

Preprint 13 p, 297.0 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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