Generic unfolding of a degenerate heterodimensional cycle

Abstract

This paper is devoted to the study of generic unfolding of a degenerate heterodimensional cycle under orbit flip condition. By setting up local moving frame systems in small tubular neighborhood of unperturbed heterodimensional cycle, we construct a Poincare return map and further obtain the bifurcation equations. Based on the bifurcation analysis, different bifurcation phenomena are discussed under small perturbations. An analytical example is also given to demonstrate our main results.