Parabolic manifolds for semi-attractive analytic transformations of $\mathbf {C}^n$
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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 $m+p+1$.References
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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
- Received by editor(s): August 8, 2008
- Received by editor(s) in revised form: June 18, 2009
- Published electronically: May 18, 2011
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 5207-5222
- MSC (2010): Primary 32H50
- DOI: https://doi.org/10.1090/S0002-9947-2011-05202-5
- MathSciNet review: 2813413