Occurrence of periodic Lame functions at bifurcations in chaotic Hamiltonian systems

URN to cite this document:: urn:nbn:de:bvb:355-epub-16601
DOI to cite this document:: 10.5283/epub.1660

Brack, Matthias ; Mehta, Mitaxi ; Tanaka, Kaori

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Date of publication of this fulltext: 05 Aug 2009 13:31

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Abstract

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 ...