Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom.
Delshams, Amadeu, Seara, Tere M. (1997)
Mathematical Physics Electronic Journal [electronic only]
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Delshams, Amadeu, Seara, Tere M. (1997)
Mathematical Physics Electronic Journal [electronic only]
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G.A. Miller (1905)
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E. Zenhder (1975)
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Boris Khesin (1993)
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F. TAKENS (1970)
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Antonio Ambrosetti, Giovanni Mancini (1981)
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Vittorio Coti Zelati, Ivar Ekeland, Eric Séré (1990)
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Carsten Thomassen (1973)
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Antonio Ambrosetti, V. Coti Zelati (1989)
Mathematische Zeitschrift
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Kazuo Okamoto (1986)
Mathematische Annalen
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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.
H. Hofer, K. Wysocki (1990)
Mathematische Annalen
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Gary Chartrand, S. F. Kapoor (1974)
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Misha Bialy, Leonid Polterovich (1992)
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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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Andrzej Szulkin (1989)
Mathematische Annalen
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