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Title: Periodic points of holomorphic maps via Lefschetz numbers
Author: Fagella Rabionet, Núria
Llibre, Jaume
Keywords: Teoria del punt fix
Aplicacions holomòrfiques
Mètodes iteratius (Matemàtica)
Fixed points and coincidences
Iteration problems
Issue Date: 2000
Publisher: American Mathematical Society
Abstract: In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.
Note: Reproducció digital del document publicat en format paper, proporcionada per JSTOR
It is part of: Transactions of the American Mathematical Society, 2000, vol. 352, núm. 10, p. 4711-4730.
ISSN: 1088-6850
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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