Hamiltonian Systems Close to Integrable Systems
E. Zenhder (1975)
Publications mathématiques et informatique de Rennes
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E. Zenhder (1975)
Publications mathématiques et informatique de Rennes
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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.
Guillaume Duval, Andrzej J. Maciejewski (2011)
Banach Center Publications
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We show how using the differential Galois theory one can find effectively necessary conditions for the integrability of Hamiltonian systems with homogeneous potentials.
Huang, Xuncheng, Tu, Guizhang (2006)
International Journal of Mathematics and Mathematical Sciences
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Boris Khesin (1993)
Recherche Coopérative sur Programme n°25
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Praught, Jeffery, Smirnov, Roman G. (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Nutku, Yavuz (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Muslih, S.I. (2002)
Journal of Applied Mathematics
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Charles-Michel Marle (2003)
Banach Center Publications
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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...
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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Ezequiel Maderna (2002)
Bulletin de la Société Mathématique de France
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We show that every global viscosity solution of the Hamilton-Jacobi equation associated with a convex and superlinear Hamiltonian on the cotangent bundle of a closed manifold is necessarily invariant under the identity component of the group of symmetries of the Hamiltonian (we prove that this group is a compact Lie group). In particular, every Lagrangian section invariant under the Hamiltonian flow is also invariant under this group.
Jianxiang Cao, Minyong Shi, Lihua Feng (2016)
Discussiones Mathematicae Graph Theory
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The balanced hypercube BHn, defined by Wu and Huang, is a variant of the hypercube network Qn, and has been proved to have better properties than Qn with the same number of links and processors. For a bipartite graph G = (V0 ∪ V1,E), we say G is edge-hyper-Hamiltonian laceable if it is Hamiltonian laceable, and for any vertex v ∈ Vi, i ∈ {0, 1}, any edge e ∈ E(G − v), there is a Hamiltonian path containing e in G − v between any two vertices of V1−i. In this paper, we prove that BHn...
Bing Wang, Xinghu Wang, Honghua Wang (2016)
Kybernetika
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In this paper, the output synchronization control is considered for multi-agent port-Hamiltonian systems with link dynamics. By using Hamiltonian energy function and Casimir function comprehensively, the design method is proposed to overcome the difficulties taken by link dynamics. The Hamiltonian function is used to handle the dynamic of agent, while the Casimir function is constructed to deal with the dynamic of link. Thus the Lyapunov function is generated by modifying the Hamiltonian...
Duca, Iulian, Udrişte, Constantin (2006)
Balkan Journal of Geometry and its Applications (BJGA)
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