Quasi-parabolic analytic transformations of Cⁿ

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• 作者：Feng Rong
• 关键词：Quasi-parabolic analytic transformations ; Parabolic curves
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2008
• 出版时间：1 July 2008
• 年：2008
• 卷：343
• 期：1
• 页码：99-109
• 全文大小：170 K

文摘

Let F be an analytic transformation of Cⁿ, with the origin O as a quasi-parabolic fixed point. We will associate an invariant, order ν(F), to F and study the local dynamics of F when it has a non-degenerate characteristic direction [v] and is dynamically separating in the direction [v]. We show that for such F there exist at least ν(F)−1 parabolic curves tangent to 39b22fd38d5caf1174017b0"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">[v] at the origin. We also study a non-dynamically-separating example in details.