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Conditions for local (reversing) symmetries in dynamical systems

Author

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

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.

Suggested Citation

  • Lamb, J.S.W. & Roberts, J.A.G. & Capel, H.W., 1993. "Conditions for local (reversing) symmetries in dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 197(3), pages 379-422.
    • Handle: RePEc:eee:phsmap:v:197:y:1993:i:3:p:379-422
    DOI: 10.1016/0378-4371(93)90592-R
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    References listed on IDEAS

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    1. Post, T. & Capel, H.W. & Quispel, G.R.W. & Van Der Weele, J.P., 1990. "Bifurcations in two-dimensional reversible maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 164(3), pages 625-662.
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    Cited by:

    1. Antonio Algaba & Cristóbal García & Jaume Giné, 2020. "Orbital Reversibility of Planar Vector Fields," Mathematics, MDPI, vol. 9(1), pages 1-25, December.
    2. Lamb, Jeroen S.W., 1996. "Area-preserving dynamics that is not reversible," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 228(1), pages 344-365.

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