Search for Periodic Orbits Appearing through Anomalous Rotation Bifurcation

Abstract

In a lecture that J.K.Moser gave in 1968, he pointed out the possibility that the periodic orbit with period q=3 (period-3 orbit) appears through anomalous rotation bifurcation (ARB). There are two different types of rotation bifurcation, the ordinary rotation bifurcation (ORB) and ARB. In order to study ORB and ARB, the map T_m (y_n+1=y_n+a(x_n−x_n^m), x_n+1=x_n+y_n+1 (a≥0, m≥2)) is introduced. It is proved that the period-3 orbit in T_m (m≥2) and the period-4 orbit in T_m (m≥3) appear through ARB and the period-4 orbit in T₂ appears through ORB.