Dijous 11 de juny, el Dipòsit Digital no estarà operatiu de 15:00 a 17:00 h per tasques de manteniment. Disculpeu les molèsties.
El jueves 11 de Junio, el Dipòsit Digital no estará operativo de 15:00 a 17:00 h debido a tareas de mantenimiento. Disculpen las molestias.
Thursday, Jun 11th, the Digital Repository will be unavailable due to a system update.

Files

146364.pdf (1.98 MB)

Document type

Article

Version

Published version

Publication date

2000

All rights reserved

Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/7765

Periodic points of holomorphic maps via Lefschetz numbers

Journal Title

Authors

Director/Tutor

Journal ISSN

Volume Title

Related resource

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.

Subject

Teoria del punt fix, Aplicacions holomòrfiques, Mètodes iteratius (Matemàtica)

Subject (English)

Fixed points and coincidences, Iteration problems

Citation

Collections

Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

FAGELLA RABIONET, Núria and LLIBRE, Jaume. Periodic points of holomorphic maps via Lefschetz numbers. Transactions of the American Mathematical Society. 2000. Vol. 352, num. 10, pags. 4711-4730. ISSN 1088-6850. [consulted: 11 of June of 2026]. Available at: https://hdl.handle.net/2445/7765

Export metadata

JSON - METS

Share record