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

摘要

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.