Chaos and maps in relativistic rynamical systems

The basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to unbounded energy. Subsequent studies have formulated the proble...

Full description

Saved in:
Bibliographic Details
Main Authors: L. P. Horwitz, Y. Ashkenazy
Format: Article
Language:English
Published: Wiley 2000-01-01
Series:Discrete Dynamics in Nature and Society
Subjects:
Online Access:http://dx.doi.org/10.1155/S1026022600000078
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850237359252045824
author L. P. Horwitz
Y. Ashkenazy
author_facet L. P. Horwitz
Y. Ashkenazy
author_sort L. P. Horwitz
collection DOAJ
description The basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistic charged particle in interaction with the electromagnetic field. We review the structure of the covariant Lorentz force used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field, establishing a connection between these equations and mass shell constraints. We argue that these relativistic generalizations of the problem are intrinsically inaccurate due to an inconsistency in the structure of the relativistic Lorentz force, and show that a reformulation of the relativistic problem, permitting variations (classically) in both the particle mass and the effective “mass” of the interacting electromagnetic field, provides a consistent system of classical equations for describing such processes.
format Article
id doaj-art-021ed1508657489c898e92a125b58340
institution OA Journals
issn 1026-0226
1607-887X
language English
publishDate 2000-01-01
publisher Wiley
record_format Article
series Discrete Dynamics in Nature and Society
spelling doaj-art-021ed1508657489c898e92a125b583402025-08-20T02:01:46ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2000-01-0141778610.1155/S1026022600000078Chaos and maps in relativistic rynamical systemsL. P. Horwitz0Y. Ashkenazy1Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel Aviv University, Ramat Aviv 69978, IsraelDepartment of Physics, Bar Ilan University, Ramat Gan 52900, IsraelThe basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistic charged particle in interaction with the electromagnetic field. We review the structure of the covariant Lorentz force used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field, establishing a connection between these equations and mass shell constraints. We argue that these relativistic generalizations of the problem are intrinsically inaccurate due to an inconsistency in the structure of the relativistic Lorentz force, and show that a reformulation of the relativistic problem, permitting variations (classically) in both the particle mass and the effective “mass” of the interacting electromagnetic field, provides a consistent system of classical equations for describing such processes.http://dx.doi.org/10.1155/S1026022600000078ChaosDynamical mapsDelativityRadiation reaction.
spellingShingle L. P. Horwitz
Y. Ashkenazy
Chaos and maps in relativistic rynamical systems
Discrete Dynamics in Nature and Society
Chaos
Dynamical maps
Delativity
Radiation reaction.
title Chaos and maps in relativistic rynamical systems
title_full Chaos and maps in relativistic rynamical systems
title_fullStr Chaos and maps in relativistic rynamical systems
title_full_unstemmed Chaos and maps in relativistic rynamical systems
title_short Chaos and maps in relativistic rynamical systems
title_sort chaos and maps in relativistic rynamical systems
topic Chaos
Dynamical maps
Delativity
Radiation reaction.
url http://dx.doi.org/10.1155/S1026022600000078
work_keys_str_mv AT lphorwitz chaosandmapsinrelativisticrynamicalsystems
AT yashkenazy chaosandmapsinrelativisticrynamicalsystems