Normal forms for singularities of one dimensional holomorphic vector fields
Abstract: We study the normal form of the ordinary differential equation $dot z=f(z)$, $zinmathbb{C}$, in a neighbourhood of a point $pinmathbb{C}$, where $f$ is a one-dimensional holomorphic function in a punctured neighbourhood of $p$. Our results include all cases except when $p$ is an essenti...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Texas State University
2004-10-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2004/122/abstr.html |
| Summary: | Abstract: We study the normal form of the ordinary differential equation $dot z=f(z)$, $zinmathbb{C}$, in a neighbourhood of a point $pinmathbb{C}$, where $f$ is a one-dimensional holomorphic function in a punctured neighbourhood of $p$. Our results include all cases except when $p$ is an essential singularity. We treat all the other situations, namely when $p$ is a regular point, a pole or a zero of order $n$. Our approach is based on a formula that uses the flow associated with the differential equation to search for the change of variables that gives the normal form. |
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| ISSN: | 1072-6691 |