Further reductions of Poincaré-Dulac normal forms in $\{\mathbf \{C\}\}^\{n+1\}$
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- by Adrian Jenkins PDF
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Abstract:
In this paper, we will consider (germs of) holomorphic mappings of the form $(f(z),\lambda _{1} w_{1}(1+g_{1}(z)),\ldots ,\lambda _{n}w_{n}(1+g_{n}(z)))$, defined in a neighborhood of the origin in ${\mathbf {C}}^{n+1}$. Most of our interest is in those mappings where $f(z)=z+a_{m}z^{m}+\cdots$ is a germ tangent to the identity and $g_{i}(0)=0$ for $i=1,\ldots ,n$, and $\lambda _{i}\in {\mathbf {C}}$ possess no resonances, for these are the so-called Poincaré-Dulac normal forms of the mappings $(z+O(2), \lambda _{1}w+O(2),\ldots ,\lambda _{n}w+O(2))$. We construct formal normal forms for these mappings and discuss a condition which tests for the convergence or divergence of the conjugating maps, giving specific examples.References
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Additional Information
- Adrian Jenkins
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47906
- Email: majenkin@math.purdue.edu
- Received by editor(s): August 28, 2006
- Received by editor(s) in revised form: December 11, 2006
- Published electronically: January 30, 2008
- Communicated by: Mei-Chi Shaw
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1671-1680
- MSC (2000): Primary 32A05, 32H50; Secondary 30D05
- DOI: https://doi.org/10.1090/S0002-9939-08-09041-2
- MathSciNet review: 2373596