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1. Cyclicity of Degenerate Polycycles Through a Saddle–Node and Two Hyperbolic Saddles.

Author

Zhao, Li

Subjects
HYPERBOLIC spaces, PERTURBATION theory, NON-Euclidean geometry, APPROXIMATION theory, FUNCTIONAL analysis, PARALLELS (Geometry)
Abstract

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 that of the other saddle is irrational. It is obtained that the cyclicity of this kind of polycycle is no more than 5 if the hp–connection keeps unbroken under the C∞ perturbations. [ABSTRACT FROM AUTHOR]

Published
2005
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