Summary
Two mechanisms terminate the sequences of period doubling bifurcations in Hamiltonian systems of 3 degrees of freedom:a) complex instability andb) inverse bifurcations. It seems that there are no infinite sequences of period-doubling bifurcations, except in systems reducible to 2 degrees of freedom.
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Contopoulos, G. Termination of sequences of bifurcation in 3-dimensional Hamiltonian systems. Lett. Nuovo Cimento 38, 257–262 (1983). https://doi.org/10.1007/BF02814640
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DOI: https://doi.org/10.1007/BF02814640