The Persistence of a Slow Manifold with Bifurcation

Kristian Uldall Kristiansen, P. Palmer, M. Robert

    Research output: Contribution to journalJournal articleResearchpeer-review


    his paper considers the persistence of a slow manifold with bifurcation in a slow-fast two degree of freedom Hamiltonian system. In particular, we consider a system with a supercritical pitchfork bifurcation in the fast space which is unfolded by the slow coordinate. The model system is motivated by tethered satellites. It is shown that an almost full measure subset of a neighborhood of the slow manifold's normally elliptic branches persists in an adiabatic sense. We prove this using averaging and a blow-up near the bifurcation.

    Original languageEnglish
    JournalS I A M Journal on Applied Dynamical Systems
    Issue number2
    Pages (from-to)661-683
    Publication statusPublished - 2012

    Bibliographical note

    Read More:


    • Singularly perturbed Hamiltonian systems
    • Slow manifolds with bifurcations
    • Pitchfork bifurcations
    • Blow-up
    • Tethered satellites


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