Codimension 3 bifurcation from orbit-flip homoclinic orbit of weak type

• Main Authors: Qiuying Lu, Guifeng Deng, Hua Luo
• Format: Article
• Language: English
• Published: University of Szeged 2015-10-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: homoclinic; orbit-flip; weak type; local moving coordinates method.
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=3968

This article is devoted to the research of a new codimension 3 homoclinic orbit bifurcation, which is the orbit-flip of weak type. Such kind of homoclinic orbit is a degenerate case of the orbit-flip homoclinic orbit. We show the existence of 1-homoclinic orbit, 1-periodic orbit, $2^n$-homoclinic orbit and $2^n$-periodic orbit for arbitrary integer $n$. Our strategy is based on the local moving coordinates method.