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    Delay Equations with Rapidly Oscillating Stable Periodic Solutions

    Stoffer, Daniel
    Journal of Dynamics and Differential Equations. - 2008/20/1/201-238
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    Plus…
    Titre: Delay Equations with Rapidly Oscillating Stable Periodic Solutions
    Auteur: Stoffer, Daniel
    Sujet: Delay differential equations - rapidly oscillating solutions - stable periodic solutions
    Description: We prove analytically that there exist delay equations admitting rapidly oscillating stable periodic solutions. Previous results were obtained with the aid of computers, only for particular feedback functions. Our proofs work for stiff equations with several classes of feedback functions. Moreover, we prove that for negative feedback there exists a class of feedback functions such that the larger the stiffness parameter is, the more stable rapidly oscillating periodic solutions there are. There are stable periodic solutions with arbitrarily many zeros per unit time interval if the stiffness parameter is chosen sufficiently large
    Publication en relation: Journal of Dynamics and Differential Equations. - 2008/20/1/201-238
    Document hôte: Journal of Dynamics and Differential Equations
    Identifiant: 10.1007/s10884-006-9068-4 (DOI)

    • Article
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    Transversal homoclinic points of the Hénon map

    Kirchgraber, Urs
    Stoffer, Daniel
    Annali di Matematica Pura ed Applicata. - 2006/185//S187-S204
    Disponible
    Plus…
    Titre: Transversal homoclinic points of the Hénon map
    Auteur: Kirchgraber, Urs
    Contributeur: Stoffer, Daniel
    Sujet: Hénon map - transversal homoclinic point - shadowing
    Description: Using shadowing techniques we prove that the Hénon map $H_{a,b}(x,y)=(a-x^{2}+by,x)$ admits a transversal homoclinic point for a set of parameters which is not small. For the area and orientation preserving Hénon map (corresponding to b=-1) we prove that a transversal homoclinic point exists for a≥0.265625. Applying a computer-assisted version of our scheme we show that the result holds even for a≥-0.866. This supports an old conjecture due to Devaney and Nitecki dating back to 1979, see [4], claiming that the Hénon map in the case b=-1 admits a transversal homoclinic point for a>-1
    Publication en relation: Annali di Matematica Pura ed Applicata. - 2006/185//S187-S204
    Document hôte: Annali di Matematica Pura ed Applicata
    Identifiant: 10.1007/s10231-004-0142-4 (DOI)

    • Plusieurs versions

    Lineare Algebra : eine Einführung für Ingenieure unter besonderer Berücksichtung numerischer Aspekte

    Nipp, Kaspar
    • Plusieurs versions

    Two results on stable rapidly oscillating periodic solutions of delay differential equations

    Stoffer, Daniel
    Dynamical Systems, 01 June 2011, Vol.26(2), pp.169-188 [Revue évaluée par les pairs]

    • Plusieurs versions

    Invariant curves for the discretised van der Pol equation

    Nipp, Kaspar, Stoffer, Daniel
    BIT Numerical Mathematics, 2017, Vol.57(2), pp.463-497 [Revue évaluée par les pairs]

    • Plusieurs versions

    Delay Equations with Rapidly Oscillating Stable Periodic Solutions

    Stoffer, Daniel
    Journal of Dynamics and Differential Equations, 2008, Vol.20(1), pp.201-238 [Revue évaluée par les pairs]

    • Plusieurs versions

    On the qualitative behaviour of symplectic integrators Part I: Perturbed linear systems

    Stoffer, Daniel
    Numerische Mathematik, 1997, Vol.77(4), pp.535-547 [Revue évaluée par les pairs]

    • Plusieurs versions

    On the Qualitative Behaviour of Symplectic Integrators. Part III. Perturbed Integrable Systems

    Stoffer, Daniel
    Journal of Mathematical Analysis and Applications, 15 January 1998, Vol.217(2), pp.521-545 [Revue évaluée par les pairs]

    • Plusieurs versions

    Transversal homoclinic points of the Hénon map

    Kirchgraber, Urs, Stoffer, Daniel
    Annali di Matematica Pura ed Applicata, 2006, Vol.185, pp.S187-S204 [Revue évaluée par les pairs]

    • Plusieurs versions

    Verification of chaotic behaviour in the planar restricted three body problem

    Stoffer, Daniel, Kirchgraber, Urs
    Applied Numerical Mathematics, 2001, Vol.39(3), pp.415-433 [Revue évaluée par les pairs]