On resonant classical Hamiltonians with n frequencies
type: Item
instance of: scholarly article
title: On resonant classical Hamiltonians with n frequencies
zbMATH Open document ID: 0711.34059
DOI: 10.1016/0022-0396(90)90057-V
author: Elsie Sterbin Gottlieb
published in: Journal of Differential Equations
publication date: 1990-01-01T00:00:00Z
review text: The author considers Hamiltonians of the quadratic forms \(H=\sum^{n}_{k=1}\omega_ kN_ k+V(Z,\bar Z),\) where \(\omega_ k\) \((k=1,2,...,n)\) are non-zero numbers, \(N_ k=| z_ k|^ 2\), \(Z=(z_ k)^ n_{k=1}\), \(\bar Z=(\bar z_ k)^ n_{k=1}\) and \(\overline{V(\bar Z,Z)}=V(Z,\bar Z)\). Here \(\bar z_ k\) denotes the complex conjugate to \(z_ k\) and \(V(Z,\bar Z)\) is a convergent power series starting with a term of order three. By studying the integrable approximation to the Hamiltonian he obtains rigorous results too complicate to be presented here, about the flow induced near the origin of the phase space.
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 4169128
zbMATH Keywords: Hamiltonians
zbMATH Keywords: phase space
MaRDI profile type: Publication
cites work: Q5559761
cites work: Q4174811
cites work: A unifying theory in determining periodic families for Hamiltonian systems at resonance
cites work: On the applicability of the third integral of motion
cites work: On resonant non linearly coupled oscillators with two equal frequencies
cites work: On resonant classical Hamiltonians with two equal frequencies
cites work: Q3862509
cites work: Q5186795
cites work: Reduction of the semisimple \(1:1\) resonance
cites work: Non-integrability of the 1:1:2–resonance
cites work: Averaging methods in nonlinear dynamical systems
cites work: Integration of near-resonant systems in slow-fluctuation approximation
cites work: Stability of constant-amplitude motions in slow-fluctuation approximation
cites work: Root parities and phase behavior in the slow-fluctuation technique
cites work: Bifurcations in the slow-fluctuation technique
cites work: On averaging, reduction, and symmetry in Hamiltonian systems
cites work: Convergent series expansions for quasi-periodic motions
cites work: On the three-dimensional lunar problem and other perturbation problems of the Kepler problem
full work available at URL: 0022-0396(90)90057-v
OpenAlex ID: W2049536546
description: scientific article; zbMATH DE number 4169128