Maciejewski A.J., Przybylska M., Tsiganov A.V. On certain classes of integrable and superintegrable homogeneous potentials, talk Workshop GDEq Integr., 11-15 Oct. 2010, Hradec nad Moravici, Czech Rep. (abstr.): Difference between revisions
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m moved Maciejewski A.J., Przybylska M., Tsiganov A.V. On certain classes of integrable and superintegrable homogeneous potentials, talk at Workshop on GDEq and Integr., 11-15 Oct. 2010, Hradec nad Moravici, Czech Rep. (abstr.) to [[Maciejewski A.J... |
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| speaker = Maria Przybylska | | speaker = Maria Przybylska | ||
| title = On certain classes of integrable and superintegrable homogeneous potentials | | title = On certain classes of integrable and superintegrable homogeneous potentials | ||
| abstract = We study the integrability of two-dimensional natural Hamiltonian systems with indefinite form of kinetic energy and homogeneous potentials of degree <math>k</math> of the form <math>H=2p_1p_2+q_1^lq_2^{k-l}</math>, where <math>k</math>, <math>l</math> | | abstract = We study the integrability of two-dimensional natural Hamiltonian systems with indefinite form of kinetic energy and homogeneous potentials of degree <math>k</math> of the form <math>H=2p_1p_2+q_1^lq_2^{k-l}</math>, where <math>k</math>, <math>l</math> are rational numbers. We show results of application of the direct method for search of first integrals. Three classes of integrable potentials are presented for that separations of variables are made and superintegrable cases are specified. In this aim some solvability results for hypergeometric equations are applied. | ||
| slides = [[Media:Maciejewski_A.J.%2C_Przybylska_M.%2C_Tsiganov_A.V._On_certain_classes_of_integrable_and_superintegrable_homogeneous_potentials_%28presentation_at_Workshop_on_Geom._Diff._Eq._and_Integrability%2C_11-15_October_2010%2C_Hradec_nad_Moravici%2C_Czech_Republic%29.pdf|Maciejewski A.J., Przybylska M., Tsiganov A.V. On certain classes of integrable and superintegrable homogeneous potentials (presentation at Workshop on Geom. Diff. Eq. and Integrability, 11-15 October 2010, Hradec nad Moravici, Czech Republic).pdf]] | | slides = [[Media:Maciejewski_A.J.%2C_Przybylska_M.%2C_Tsiganov_A.V._On_certain_classes_of_integrable_and_superintegrable_homogeneous_potentials_%28presentation_at_Workshop_on_Geom._Diff._Eq._and_Integrability%2C_11-15_October_2010%2C_Hradec_nad_Moravici%2C_Czech_Republic%29.pdf|Maciejewski A.J., Przybylska M., Tsiganov A.V. On certain classes of integrable and superintegrable homogeneous potentials (presentation at Workshop on Geom. Diff. Eq. and Integrability, 11-15 October 2010, Hradec nad Moravici, Czech Republic).pdf]] | ||
| references = | | references = | ||
| 79YY-MM-DD = 7989-89-85 | | 79YY-MM-DD = 7989-89-85 | ||
}} | }} | ||
Latest revision as of 22:42, 16 April 2011
Speaker: Maria Przybylska
Title: On certain classes of integrable and superintegrable homogeneous potentials
Abstract:
We study the integrability of two-dimensional natural Hamiltonian systems with indefinite form of kinetic energy and homogeneous potentials of degree of the form , where , are rational numbers. We show results of application of the direct method for search of first integrals. Three classes of integrable potentials are presented for that separations of variables are made and superintegrable cases are specified. In this aim some solvability results for hypergeometric equations are applied.
