A class of Hamiltonian systems with increasing periods.
Renate Schaaf (1985)
Journal für die reine und angewandte Mathematik
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Renate Schaaf (1985)
Journal für die reine und angewandte Mathematik
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E. Zenhder (1975)
Publications mathématiques et informatique de Rennes
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Thomas Bartsch, Michel Willem (1994)
Journal für die reine und angewandte Mathematik
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Boris Khesin (1993)
Recherche Coopérative sur Programme n°25
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Nutku, Yavuz (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Misha Bialy, Leonid Polterovich (1992)
Mathematische Annalen
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Zhu Daxin (1991)
Manuscripta mathematica
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Polterovich, Leonid (1998)
Documenta Mathematica
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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.
Gary Chartrand, S. F. Kapoor (1974)
Colloquium Mathematicae
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Demovič, A. (1995)
Acta Mathematica Universitatis Comenianae. New Series
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Takuo Fukuda, Stanisław Janeczko (2008)
Banach Center Publications
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The notion of an implicit Hamiltonian system-an isotropic mapping H: M → (TM,ω̇) into the tangent bundle endowed with the symplectic structure defined by canonical morphism between tangent and cotangent bundles of M-is studied. The corank one singularities of such systems are classified. Their transversality conditions in the 1-jet space of isotropic mappings are described and the corresponding symplectically invariant algebras of Hamiltonian generating functions are calculated. ...
Hüseyin Kocak (1984)
Monatshefte für Mathematik
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Huang, Xuncheng, Tu, Guizhang (2006)
International Journal of Mathematics and Mathematical Sciences
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Jens-P. Bode, Anika Fricke, Arnfried Kemnitz (2015)
Discussiones Mathematicae Graph Theory
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In 1980 Bondy [2] proved that a (k+s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1)(n+s−1)+1)/2. It is shown in [1] that one can allow exceptional (k+ 1)-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity...
Patricio L. Felmer (1990)
Manuscripta mathematica
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Praught, Jeffery, Smirnov, Roman G. (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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