Results 201 to 210 of about 129,282 (240)

Topology, singularities and integrability in Hamiltonian systems with two degrees of freedom

Izvestiya: Mathematics, 2017
Summary: We consider the problem of the existence of first integrals that are polynomial in momenta for Hamiltonian systems with two degrees of freedom on a fixed energy level (conditional Birkhoff integrals). It is assumed that the potential has several singular points.
Bolotin, Sergey V., Kozlov, Valery V.
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Integrable Hamiltonian Systems with Two Degrees of Freedom

1997
Our main goal in this chapter is to describe the structure of the Liouville foliation near a singular fiber of an integrable Hamiltonian system (definitions follow). A similar problem was formulated by S. Smale [1970]. Here we discuss some new results in this direction obtained by L. Lerman and Ya. Umanskii [1987: 1993], by A. Bolsinov [1991], and by V.
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Non-Pfaffian quasi-bi-Hamiltonian systems with two degrees of freedom

Journal of Physics A: Mathematical and General, 1998
To reveal integrability of a Hamiltonian system the author proposed before to search for a so-called quasi-bi-Hamiltonian structure, that is, the Hamiltonian vector field, after multiplication by some smooth function (integrating factor) should be also a Hamiltonian but with respect to another Poisson bracket compatible with the initial one.
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A necessary condition for the integrability of homogeneous Hamiltonian systems with two degrees of freedom

Journal of Physics A: Mathematical and General, 2001
Summary: A necessary condition for the integrability of Hamiltonian systems with a two-dimensional homogeneous potential, due to \textit{J. J. Morales-Ruiz} and \textit{J. P. Ramis} [Methods Appl. Anal. 8, No. 1, 113--120 (2001; Zbl 1140.37353)], is extended for more general Hamiltonian systems of the form \(H=T(p_1,p_2) + V(q_1,q_2)\), with ...
Nakagawa, Katsuya, Yoshida, Haruo
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Large excursions of action within the resonance of a degenerate Hamiltonian system with two degrees of freedom

Physical Review E, 2009
We investigate the width of the resonance zone in a degenerate Hamiltonian system with two degrees of freedom, in which the Hamiltonian lacks the quadratic term in the Taylor expansion. This leads to larger excursions of action in the phase space than the nondegenerate one, and corresponding resonance frequency widths would become narrower. However, in
Jian, Li, Wei-Dong, Li, Jie, Liu, Yi-Sui, Sun   +3 more
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Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity

Russian Mathematical Surveys, 1990
CONTENTS § 1. Introduction § 2. Realizability theorem § 3. Tagged skeletons § 4.
A V Bolsinov, S V Matveev, A T Fomenko
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Non-linear oscillations of a Hamiltonian system with two degrees of freedom with 2:1 resonance

Journal of Applied Mathematics and Mechanics, 2010
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A smooth trajectory classification of integrable Hamiltonian systems with two degrees of freedom

Sbornik: Mathematics, 1995
Summary: We construct an invariant of integrable Hamiltonian systems with two degrees of freedom (the so-called st-molecule) enabling such systems to be classified on three-dimensional constant-energy surfaces up to orientation-preserving diffeomorphisms taking trajectories into trajectories. This continues research of the author and \textit{A.
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Periodic Orbit-Dividing Surfaces in Rotating Hamiltonian Systems with Two Degrees of Freedom

International Journal of Bifurcation and Chaos
In this paper, we extend the notion of periodic orbit-dividing surfaces (PODS) to rotating Hamiltonian systems with two degrees of freedom. First, we present a method that enables us to apply the classical algorithm for the construction of PODS [ Pechukas & McLafferty ,  1973 ;  Pechukas ,  1981 ;  Pollak & Pechukas ,  1978 ;  Pollak ,  1985 ]
Matthaios Katsanikas, Stephen Wiggins
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The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom

Journal of Applied Mathematics and Mechanics, 2013
Abstract The stability of the equilibrium position at the origin of coordinates of a Hamiltonian system with two degrees of freedom with a Hamiltonian, the unperturbed part of which generates oscillators with a cubic restoring force, is considered. It is proved that the equilibrium position is Lyapunov conditionally stable for initial values which do
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