Bifurcations of snap-back repellers with application to border-collision bifurcations

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    The bifurcation theory of snap-back repellers in hybrid dynamical systems is developed. Infinite sequences of bifurcations are shown to arise due to the creation of snap-back repellers in noninvertible maps. These are analogous to the cascades of bifurcations known to occur close to homoclinic tangencies for diffeomorphisms. The theoretical results are illustrated with reference to bifurcations in the normal form for border-collision bifurcations. © 2010 World Scientific Publishing Company.
    Original languageEnglish
    Pages (from-to)479-489
    Number of pages10
    JournalInternational Journal of Bifurcation and Chaos
    Issue number2
    Publication statusPublished - Feb 2010


    • Border-collision bifurcation
    • Hybrid system
    • Snap-back-repeller


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