Cyclicity of degenerate polycycles through a saddle-node and two hyperbolic saddles (Q2581173)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cyclicity of degenerate polycycles through a saddle-node and two hyperbolic saddles |
scientific article |
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Cyclicity of degenerate polycycles through a saddle-node and two hyperbolic saddles (English)
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9 January 2006
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This paper deals with the cyclicity of a kind of degenerate planar polycycles through a saddle-node and two hyperbolic saddles, where the hyperbolicity ratio of the saddle which connects the saddle-node with hp-connection is equal to 1 and the ratio of the other saddle is irrational. The author proves that the cyclicity of such kind of polycycles is at most 5 if the hp-connection persists under an infinitely-smooth perturbation.
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planar vector field
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degenerate polycycle
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hp-connection
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cyclicity
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finitely-smooth normal form
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transition map
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