On dynamical systems close to a product of m rotations

Patrick Bonckaert, Timoteo Carletti, Ernest Fontich

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    Abstract

    We consider analytic one parameter families of vector fields and diffeomorphisms, including for a parameter value, the product of rotations in R2m × Rn such that for positive values of the parameter the origin is a hyperbolic point of saddle type. We address the question of determining the limit stable invariant manifold when \epsilon goes to zero as a subcenter invariant manifold when \epsilon = 0
    Original languageEnglish
    Pages (from-to)349-366
    Number of pages18
    JournalDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
    Volume24
    Issue number2
    Publication statusPublished - Jun 2009

    Keywords

    • subcenter invariant manifolds
    • Perturbations of rotations
    • bifurcations

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