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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

From an iteration formula to Poincaré's Isochronous Center Theorem for holomorphic vector fields


Author: Guang Yuan Zhang
Journal: Proc. Amer. Math. Soc. 135 (2007), 2887-2891
MSC (2000): Primary 32H50, 32M25, 37C27
Published electronically: May 8, 2007
MathSciNet review: 2317965
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Abstract | References | Similar Articles | Additional Information

Abstract: We first generalize a classical iteration formula for one variable holomorphic mappings to a formula for higher dimensional holomorphic mappings. Then, as an application, we give a short and intuitive proof of a classical theorem, due to H. Poincaré, for the condition under which a singularity of a holomorphic vector field is an isochronous center.


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Additional Information

Guang Yuan Zhang
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
Email: gyzhang@math.tsinghua.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08802-8
PII: S 0002-9939(07)08802-8
Keywords: Ordinary differential equation, holomorphic differential equation
Received by editor(s): November 23, 2005
Received by editor(s) in revised form: May 30, 2006
Published electronically: May 8, 2007
Additional Notes: The author is supported by Chinese NSFC 10271063 and 10571009
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.