A general background of higher order geometry and induced objects on subspaces.
Popescu, Marcela, Popescu, Paul (2002)
Balkan Journal of Geometry and its Applications (BJGA)
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Popescu, Marcela, Popescu, Paul (2002)
Balkan Journal of Geometry and its Applications (BJGA)
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Robert Gębarowski (2011)
Banach Center Publications
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Hydrogen atoms placed in external fields serve as a paradigm of a strongly coupled multidimensional Hamiltonian system. This system has been already very extensively studied, using experimental measurements and a wealth of theoretical methods. In this work, we apply the Morales-Ramis theory of non-integrability of Hamiltonian systems to the case of the hydrogen atom in perpendicular (crossed) static electric and magnetic uniform fields.
Muslih, S.I. (2002)
Journal of Applied Mathematics
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E. Zenhder (1975)
Publications mathématiques et informatique de Rennes
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Echeverría-Enríquez, A., Muñoz-Lecanda, M.C., Román-Roy, N. (2002)
International Journal of Mathematics and Mathematical Sciences
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Chavchanidze, G. (2003)
Georgian Mathematical Journal
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Boris Khesin (1993)
Recherche Coopérative sur Programme n°25
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Henryk Żołądek (2011)
Banach Center Publications
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The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.
Popescu, Paul, Popescu, Marcela (2002)
Balkan Journal of Geometry and its Applications (BJGA)
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Nutku, Yavuz (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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L. Polterovich, M. Bialy (1992)
Geometric and functional analysis
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Xavier Gràcia, Josep M. Pons (1996)
Extracta Mathematicae
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Praught, Jeffery, Smirnov, Roman G. (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Udrişte, Constantin, Teleman, Ana-Maria (2004)
International Journal of Mathematics and Mathematical Sciences
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