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

 

Fixed point indices and invariant periodic sets of holomorphic systems


Author: Guang Yuan Zhang
Journal: Proc. Amer. Math. Soc. 135 (2007), 767-776
MSC (2000): Primary 32H50, 32M25, 37C25
Published electronically: October 2, 2006
MathSciNet review: 2262872
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Abstract: This note presents an intuitive method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will prove Needham's theorem in a more general version.


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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, gyzhang@mail.tsinghua.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08821-6
PII: S 0002-9939(06)08821-6
Keywords: Fixed point index, ordinary differential equation, holomorphic differential equation
Received by editor(s): May 15, 2005
Received by editor(s) in revised form: October 7, 2005
Published electronically: October 2, 2006
Additional Notes: The author was supported by Chinese NSFC 10271063 and 10571009
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.