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From an iteration formula to Poincaré's Isochronous Center Theorem for holomorphic vector fields
Author(s):
Guang
Yuan
Zhang
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2887-2891.
MSC (2000):
Primary 32H50, 32M25, 37C27
Posted:
May 8, 2007
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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:
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
Posted:
May 8, 2007
Additional Notes:
The author is supported by Chinese NSFC 10271063 and 10571009
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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