Orbital behaviour transition from the Henon-Heiles to the three-particle Toda lattice Hamiltonian
type: Item
instance of: scholarly article
title: Orbital behaviour transition from the Henon-Heiles to the three-particle Toda lattice Hamiltonian
zbMATH Open document ID: 0706.70030
DOI: 10.1016/0167-2789(90)90047-S
author: S. Udry
author: L. Martinet
published in: Physica D
publication date: 1990-01-01T00:00:00Z
review text: For the n-order approximations \(H_ n\) of the three particle Toda lattice, plots of orbits on sections and of Lyapunov exponents of periodic orbits are presented for \(n\leq 3\leq 10\), and for the standard homotopy \(\epsilon \mapsto H_{34}(\epsilon)\) between \(H_ 3\) and \(H_ 4\), \(H_{34}(\epsilon)=H_ 3+\epsilon (H_ 4-H_ 3)\), \(0\leq \epsilon \leq 1\), at various energy levels. These plots are discussed in detail, directing attention to (perceptible) transitions from regular to chaotic behaviour.
Mathematics Subject Classification ID: 70K50
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 4160203
zbMATH Keywords: three particle Toda lattice
zbMATH Keywords: orbits on sections
zbMATH Keywords: Lyapunov exponents of periodic orbits
zbMATH Keywords: standard homotopy
zbMATH Keywords: chaotic behaviour
reviewed by: Hans Crauel
MaRDI profile type: Publication
cites work: Approximations of the 3-particle Toda lattice
cites work: Non-integrability of the fourth-order truncated Toda Hamiltonian
cites work: Non-integrability of the truncated Toda lattice Hamiltonian at any order
cites work: The stability of periodic orbits in the three-body problem
cites work: Universal behaviour in families of area-preserving maps
cites work: Integrals of the Toda lattice
full work available at URL: 0167-2789(90)90047-s
OpenAlex ID: W2046100870
description: scientific article; zbMATH DE number 4160203