Commutativity of flows and injectivity of nonsingular mappings

M. Sabatini

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Displaying similar documents to “Commutativity of flows and injectivity of nonsingular mappings”

On variants of Arnold conjecture

Roman Golovko (2020)

Archivum Mathematicum

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In this note we discuss the collection of statements known as Arnold conjecture for Hamiltonian diffeomorphisms of closed symplectic manifolds. We provide an overview of the homological, stable and strong versions of Arnold conjecture for non-degenerate Hamiltonian systems, a few versions of Arnold conjecture for possibly degenerate Hamiltonian systems, the degenerate version of Arnold conjecture for Hamiltonian homeomorphisms and Sandon’s version of Arnold conjecture for contactomorphisms. ...

On the construction of a $C^{2}$ -counterexample to the Hamiltonian Seifert conjecture in $ℝ^{4}$ .

Ginzburg, Viktor L., Gürel, Basak Z. (2002)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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Chvátal-Erdös type theorems

Jill R. Faudree, Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson, Colton Magnant (2010)

Discussiones Mathematicae Graph Theory

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The Chvátal-Erdös theorems imply that if G is a graph of order n ≥ 3 with κ(G) ≥ α(G), then G is hamiltonian, and if κ(G) > α(G), then G is hamiltonian-connected. We generalize these results by replacing the connectivity and independence number conditions with a weaker minimum degree and independence number condition in the presence of sufficient connectivity. More specifically, it is noted that if G is a graph of order n and k ≥ 2 is a positive integer such that κ(G) ≥ k, δ(G) >...

On solvmanifolds and a conjecture of Benson and Gordon from the Hamiltonian viewpoint.

Tralle, Aleksy, Andrzejewski, Wojciech (1998)

Journal of Lie Theory

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Hamiltonian Dynamics on Pseudodifferential Symbols

Boris Khesin (1993)

Recherche Coopérative sur Programme n°25

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Hamiltonian Systems Close to Integrable Systems

E. Zenhder (1975)

Publications mathématiques et informatique de Rennes

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On the classical non-integrability of the Hamiltonian system for hydrogen atoms in crossed electric and magnetic fields

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.

A simple proof of the non-integrability of the first and the second Painlevé equations

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.

On singularities of Hamiltonian mappings

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. ...

Improved Sufficient Conditions for Hamiltonian Properties

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...

Hamiltonian square roots of skew Hamiltonian quaternionic matrices.

Rodman, Leiba (2008)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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A note on the Hamiltonian genus of a complete bipartite graph.

Demovič, A. (1995)

Acta Mathematica Universitatis Comenianae. New Series

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The Weinstein Conjecture in P X Cl.

H. Hofer, A. Floer, C. Viterbo (1990)

Mathematische Zeitschrift

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On Hamiltonian properties of powers of special Hamiltonian graphs

Gary Chartrand, S. F. Kapoor (1974)

Colloquium Mathematicae

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Output synchronization of multi-agent port-Hamiltonian systems with link dynamics

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...

A note on the Song-Zhang theorem for Hamiltonian graphs

Kewen Zhao, Ronald J. Gould (2010)

Colloquium Mathematicae

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An independent set S of a graph G is said to be essential if S has a pair of vertices that are distance two apart in G. In 1994, Song and Zhang proved that if for each independent set S of cardinality k+1, one of the following condition holds: (i) there exist u ≠ v ∈ S such that d(u) + d(v) ≥ n or |N(u) ∩ N(v)| ≥ α (G); (ii) for any distinct u and v in S, |N(u) ∪ N(v)| ≥ n - max{d(x): x ∈ S}, then G is Hamiltonian. We prove that if for each...

The Birkhoff-Lewis Fixed Point Theorem and a Conjecture of V.I. Arnold.

C.C. Conley, E. Zehnder (1983)

Inventiones mathematicae

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