Brack, Matthias and Mehta, Mitaxi and Tanaka, Kaori
Occurrence of periodic Lame functions at bifurcations in chaotic Hamiltonian systems.
Journal of Physics A 34 (40), pp. 8199-8220.
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Other URL: http://www.iop.org/EJ/abstract/0305-4470/34/40/301
We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset of chaos, are given analytically by the periodic solutions of the Lame equation as classified in 1940 by Ince. In Hamiltonians with C_2v symmetry, they occur ...
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