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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Parabolic manifolds for semi-attractive analytic transformations of $ \mathbf{C}^n$


Author: Feng Rong
Journal: Trans. Amer. Math. Soc. 363 (2011), 5207-5222
MSC (2010): Primary 32H50
Published electronically: May 18, 2011
MathSciNet review: 2813413
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Abstract: We study the local dynamics of semi-attractive analytic transformations of $ \mathbf{C}^n$. Under certain assumptions, Rivi showed the existence of parabolic manifolds of dimension $ m+1$, where $ m$ is the number of eigenvalues with modulus strictly less than one. Assuming moreover that certain matrix has $ p$ eigenvalues with positive real part, we show the existence of parabolic manifolds of dimension $ m+p+1$.


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Additional Information

Feng Rong
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
Address at time of publication: Department of Mathematics, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05202-5
PII: S 0002-9947(2011)05202-5
Received by editor(s): August 8, 2008
Received by editor(s) in revised form: June 18, 2009
Published electronically: May 18, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.