HOMOCLINIC BIFURCATIONS WITH NONHYPERBOLIC EQUILIBRIA

Authors

Bo Deng, University of Nebraska-LincolnFollow

Date of this Version

5-15-1989

Citation

1990 Society for Industrial and Applied Mathematics

Comments

SIAM J. MATH. ANAL. Vol. 21, No. 3, pp. 693-720, May 1990

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.