Further reductions of Poincaré-Dulac normal forms in  <IMG WIDTH="53" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="/proc/2008-136-05/S0002-9939-08-09041-2/gif-title0/img1.gif" ALT="$ {\mathbf{C}}^{n+1}$">期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Further reductions of Poincaré-Dulac normal forms in ${\mathbf{C}}^{n+1}$

Authors:	Adrian Jenkins

Institution:	Department of Mathematics, Purdue University, West Lafayette, Indiana 47906

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.

Keywords:	Holomorphic mappings conjugacy equivalence

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