Connections to fixed points and Sil’nikov saddle-focus homoclinic orbits in singularly perturbed systems

• Published in: Український математичний журнал
• Date: 2008
• Main Authors: Battelli, F., Palmer, K.J.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/164249
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Connections to fixed points and Sil’nikov saddle-focus homoclinic orbits in singularly perturbed systems / F. Battelli, K.J. Palmer // Український математичний журнал. — 2008. — Т. 60, № 1. — С. 28–55. — Бібліогр.: 21 назв. — англ.

We consider a singularly perturbed system depending on two parameters with two (possibly the same) normally hyperbolic centre manifolds. We assume that the unperturbed system has an orbit connecting a hyperbolic fixed point on one centre manifold to a hyperbolic fixed point on the other. Then we p...