Bifurcations in two-dimensional reversible maps

T. Post, H.W. Capel, G.R.W. Quispel, J.P. van der Weele

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    Abstract

    We give a treatment of the non-resonant bifurcations involving asymmetric fixed points with Jacobian J≠1 in reversible mappings of the plane. These bifurcations include the saddle-node bifurcation not in the neighbourhood of a fixed point with J≠1, as well as the so-called transcritical bifurcations and generalized Rimmer bifurcations taking place at a fixed point with Jacobian J≠1. The bifurcations are illustrated by some simple examples of model maps. The Rimmer type of bifurcation, with e.g. a center point with J≠1 changing into a saddle with Jacobian J≠1, an attractor and a repeller, occurs under more general conditions, i.e. also in non-reversible mappings if only a certain order of local reversibility is satisfied. These Rimmer bifurcations are important in connection with the emergence of dissipative features in non-measure-preserving reversible dynamical systems.
    Original languageUndefined
    Pages (from-to)625-662
    Number of pages38
    JournalPhysica A
    Volume164
    Issue number3
    DOIs
    Publication statusPublished - 1990

    Keywords

    • IR-72890
    • METIS-129598

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