REVERSING K-SYMMETRIES IN DYNAMICAL-SYSTEMS

Citation
Jsw. Lamb et Grw. Quispel, REVERSING K-SYMMETRIES IN DYNAMICAL-SYSTEMS, Physica. D, 73(4), 1994, pp. 277-304
Citations number
40
Categorie Soggetti
Mathematical Method, Physical Science",Physics,"Physycs, Mathematical
Journal title
ISSN journal
01672789
Volume
73
Issue
4
Year of publication
1994
Pages
277 - 304
Database
ISI
SICI code
0167-2789(1994)73:4<277:RKID>2.0.ZU;2-Y
Abstract
We generalize the concept of (reversing) symmetries of a dynamical sys tem, i.e. we study dynamical systems that possess symmetry properties only if considered on a proper time scale. In particular (considering dynamical systems with discrete time), the kth iterate of a map may po ssess more (reversing) symmetries than the map itself. In this way the concepts of (reversing) symmetries and (reversing) symmetry groups ar e generalized to (reversing) k-symmetries and (reversing) k-symmetry g roups. Furthermore, a method is studied for finding orbits that are (k -) symmetric with respect to reversing (k-)-symmetries. Firstly an exi sting method for finding orbits that are symmetric with respect to one reversing symmetry is extended to the case of more than one reversing symmetry and secondly a generalization of this method to the case of reversing k-symmetries is introduced. Some physically relevant example s of dynamical systems possessing reversing k-symmetries are discussed briefly.