Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip*

Abstract

Heteroclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a principal heteroclinic orbit and a non-principal heteroclinic orbit that takes orbit flip. The existence, nonexistence, coexistence and uniqueness of the 1-heteroclinic loop, 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold or three-fold 1-periodic orbit is also obtained.

Keywords

Bifurcation / Heteroclinic loop / Non-resonance / Orbit flip / Periodic orbit / 34C37 / 37C29 / 34C23

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