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...
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Wiley
2000-01-01
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| Series: | Discrete Dynamics in Nature and Society |
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| Online Access: | http://dx.doi.org/10.1155/S1026022600000078 |
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| 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 |