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Orbital topological classification of analytic differential equations in a neighborhood of a degenerate elementary singular point on the two-dimensional complex plane

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Abstract

We consider the germ of an analytic differential equation in (C2, 0) defined by a vector field with a singularity at zero. A singular point of the equation is called degenerate elementary if one eigenvalue of the linear part of the field is equal to zero and the other is different from zero. The orbital topological classification of differential equations in a neighborhood of a degenerate elementary singular point is obtained for all cases except the so-called “Liouville” case. This case defines a subset of equations which does not separate the corresponding function space.

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Authors
  1. P. M. Elizarov
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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 13, pp. 137–165, 1988.

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Elizarov, P.M. Orbital topological classification of analytic differential equations in a neighborhood of a degenerate elementary singular point on the two-dimensional complex plane. J Math Sci 50, 1447–1468 (1990). https://doi.org/10.1007/BF01388508

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  • DOI: https://doi.org/10.1007/BF01388508

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