Maciejewski A. Necessary conditions for super-integrabilityily, talk at Workshop on GDEq and Integrability, 11-15 Oct. 2010, Hradec nad Moravici, Czech Rep. (abstract): Difference between revisions
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| speaker = Andrzej Maciejewski | | speaker = Andrzej Maciejewski | ||
| title = Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces | | title = Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces | ||
| abstract = We formulate the necessary conditions for the maximal super-integrability of certain family of classical potentials defined in the constant curvature two-dimensional spaces. We give examples of homogeneous potentials of degree <math> | | abstract = We formulate the necessary conditions for the maximal super-integrability of certain family of classical potentials defined in the constant curvature two-dimensional spaces. We give examples of homogeneous potentials of degree <math>-2</math> on Euclidean plane as well as their equivalents on sphere and the hyperbolic plane for which these necessary conditions are also sufficient. We show explicit forms of the additional first integrals which always can be chosen polynomial with respect to the momenta and which can be of an arbitrary high degree with respect to the momenta. | ||
| slides = [[Media:Maciejewski_A._Necessary_conditions_for_classical_super-integrability_of_a_certain_family_of_potentials_in_constant_curvature_spaces_%28presentation_at_Workshop_Geom._Diff._Eq._and_Integrability%2C_11-15_October_2010%2C_Hradec_nad_Moravici%2C_Czech_Rep.%29.pdf|Maciejewski A. Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces (presentation at Workshop Geom. Diff. Eq. and Integrability, 11-15 October 2010, Hradec nad Moravici, Czech Rep.).pdf]] | | slides = [[Media:Maciejewski_A._Necessary_conditions_for_classical_super-integrability_of_a_certain_family_of_potentials_in_constant_curvature_spaces_%28presentation_at_Workshop_Geom._Diff._Eq._and_Integrability%2C_11-15_October_2010%2C_Hradec_nad_Moravici%2C_Czech_Rep.%29.pdf|Maciejewski A. Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces (presentation at Workshop Geom. Diff. Eq. and Integrability, 11-15 October 2010, Hradec nad Moravici, Czech Rep.).pdf]] | ||
| references = | | references = | ||
| 79YY-MM-DD = 7989-89-85 | | 79YY-MM-DD = 7989-89-85 | ||
}} | }} | ||
Latest revision as of 22:35, 16 April 2011
Speaker: Andrzej Maciejewski
Title: Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces
Abstract:
We formulate the necessary conditions for the maximal super-integrability of certain family of classical potentials defined in the constant curvature two-dimensional spaces. We give examples of homogeneous potentials of degree on Euclidean plane as well as their equivalents on sphere and the hyperbolic plane for which these necessary conditions are also sufficient. We show explicit forms of the additional first integrals which always can be chosen polynomial with respect to the momenta and which can be of an arbitrary high degree with respect to the momenta.