First integrals that are polynomial in momenta for a mechanical system on a two-dimensional torus
type: Item
instance of: scholarly article
title: First integrals that are polynomial in momenta for a mechanical system on a two-dimensional torus
zbMATH Open document ID: 0668.58014
DOI: 10.1007/BF01077805
author: M. L. Byalyĭ
publication date: 1987-01-01T00:00:00Z
review text: Let \(H=(p^ 2_ 1+p^ 2_ 2)/2+V(x,y)\) be a Hamiltonian function on a torus with the Cartesian coordinates \(x,y\). The author finds the functions \(V\) such that first integrals which are polynomials of degree \(1,2,3,4\) in \((p_ 1,p_ 2)\) exist. These functions are the same for degrees \(3,1\) on the one hand, and \(4,2\) on the other.
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 37J35
zbMATH DE Number: 4094427
zbMATH Keywords: first integrals
zbMATH Keywords: mechanical systems
zbMATH Keywords: Hamiltonian function
reviewed by: Izu Vaisman
MaRDI profile type: Publication
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4094427