Conditions for local (reversing) symmetries in dynamical systems

J.S.W. Lamb, J.A.G. Roberts and H.W. Capel

Physica A: Statistical Mechanics and its Applications, 1993, vol. 197, issue 3, 379-422

Abstract: Dynamical systems may possess symmetries and reversing symmetries. Local (reversing) symmetries around fixed points of dynamical systems are characterized, as a property of their normal form expansions. In this paper an inductive method is introduced to derive conditions for a fixed point to possess a local (reversing) symmetry of finite order. The method is introduced for dynamical systems with continuous time (flows). The analogous problem for dynamical systems with discrete time (mappings) is discussed afterwards. Conditions for local (reversing) symmetries are given explicitly for fixed points of planar flows. These conditions may be used as a negative criterion to show that a given dynamical system does not have a (reversing) symmetry.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:197:y:1993:i:3:p:379-422

DOI: 10.1016/0378-4371(93)90592-R

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