Displaying similar documents to “The HELP inequality for Hamiltonian systems.”

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

Henryk Żołądek (2011)

Banach Center Publications

Similarity:

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.

Andrew Lenard: a mystery unraveled.

Praught, Jeffery, Smirnov, Roman G. (2005)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Similarity:

Improved Sufficient Conditions for Hamiltonian Properties

Jens-P. Bode, Anika Fricke, Arnfried Kemnitz (2015)

Discussiones Mathematicae Graph Theory

Similarity:

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...

Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval

Roman Šimon Hilscher, Petr Zemánek (2010)

Mathematica Bohemica

Similarity:

In this paper we consider a linear operator on an unbounded interval associated with a matrix linear Hamiltonian system. We characterize its Friedrichs extension in terms of the recessive system of solutions at infinity. This generalizes a similar result obtained by Marletta and Zettl for linear operators defined by even order Sturm-Liouville differential equations.