Structures in the phase space of a four dimensional symplectic map
type: Item
instance of: scholarly article
title: Structures in the phase space of a four dimensional symplectic map
zbMATH Open document ID: 0884.58051
DOI: 10.1007/BF00053508
author: O. Diekmann
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1998-04-01T00:00:00Z
review text: There are a lot of scientists interested in equivalently Hamiltonian systems of two degrees of freedom, also called two-dimensional symplectic maps \((2-\Delta)\), but there are just a few who successfully investigated the behavior of higher dimensional systems. Among htese are the authors of the present paper. They consider that it is of high interest to find the types of structures that exist in a \(4-\Delta\) phase space. Therefore, the authors numerically investigate the projections of nonperiodic orbits in a \(4-\Delta\) symplectic map composed of two-coupled \(2-\Delta\) maps. They also give a detailed description of the structures that are produced in different planes of projection and they find how the morphology of the \(4-\Delta\) orbits is influenced by the featues of the \(2-\Delta\) maps when the coupling parameter increases. Moreover, the authors succeed to give an empirical law that describes this influence. Briefly, the main result of the paper consists in the fact that the \(2-\Delta\) maps strongly influence the \(4-\Delta\) case and the existence of well defined structures in the projections of the \(2-\Delta\) tori.
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 1051297
zbMATH Keywords: \(4-\Delta\) symplectic maps
zbMATH Keywords: nonperiodic orbits
zbMATH Keywords: phase space structures
zbMATH Keywords: resonances
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00053508
OpenAlex ID: W1979717212
description: scientific article; zbMATH DE number 1051297