Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
30 (1989), S. 2214-2225
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The effect of enlarging the class of admissible movable singularities in Painlevé analysis to include all rational algebraic branch points is examined for a class of quartic polynomial potentials. Eight homogeneous quartic potentials are found in addition to the seven integrable cases given by weak Painlevé analysis. They are examined using various numerical techniques and Ziglin's theorem. Only one of them remains a candidate for integrability, which indicates that, in general, most rational algebraic branch points are incompatible with integrability. Movable logarithmic singularities also appear to be inconsistent with integrability. However, the remaining potentials are either regular or nearly regular for the energies examined, and are therefore still of interest for numerical purposes. The corresponding surfaces of section are found to be particularly simple in structure and belong to a small number of topologically distinct classes. Their stable and unstable periodic orbit structures are examined to provide information about their regularity and for use in Ziglin's theorem. There appears to be a correlation between the resonances of the stable periodic orbits and the order of the corresponding movable singularities.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.528546
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