Abstract

There are many infinite sequences of period doubling bifurcations of families of periodic orbits in conservative Hamiltonian systems. In systems of two degrees of freedom, the bifurcation ratio has the universal value 6=8.72. In rotating systems these infinite bifurcations are followed by inverse bifurcations, forming an infinity of bubbles. In systems of three degrees of freedom (that cannot be reduced to a 2-D system plus an independent oscillation) it seems that there are no infinite sequences of bifurcations. The bifurcation sequences terminate either by complex instability or by inverse bifurcation.

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