Mathematics, Department of
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Document Type
Article
Date of this Version
5-15-1989
Citation
1990 Society for Industrial and Applied Mathematics
Abstract
A general geometric approach is given for bifurcation problems with homoclinic orbits to nonhyperbolic equilbrium points of ordinary differential equations. It consists of a special normal form called admissible variables, exponential expansion, strong A-lemma, and Lyapnunov- Schmidt reduction for the Poincare maps under Sil'nikov variables. The method is based on the Center Manifold Theory, the contraction mapping principle, and the Implicit Function Theorem.
Comments
SIAM J. MATH. ANAL. Vol. 21, No. 3, pp. 693-720, May 1990