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Peter Albers

  1. Global surfaces of section in the planar restricted 3-body problem.

    Tue, 03/22/2011 - 16:01 — SomNambul
    Authors: Urs Frauenfelder, Joel W. Fish, Peter Albers, Helmut Hofer, Otto van Koert
    Subjects: Symplectic Geometry
    Abstract

    The restricted planar three-body problem has a rich history, yet many
    unanswered questions still remain. In the present paper we prove the existence
    of a global surface of section near the smaller body in a new range of energies
    and mass ratios for which the Hill's region still has three connected
    components. The approach relies on recent global methods in symplectic geometry
    and contrasts sharply with the perturbative methods used until now.

  2. Periodic bounce orbits of prescribed energy.

    Tue, 06/08/2010 - 15:01 — SomNambul
    Authors: Peter Albers, Marco Mazzucchelli
    Subjects: Dynamical Systems
    Abstract

    We prove the existence of periodic bounce orbits of prescribed energy on an
    open bounded domain in Euclidean space. We derive explicit bounds on the period
    and the number of bounce points.

  3. Cup-length estimates for leaf-wise intersections.

    Thu, 02/18/2010 - 16:01 — SomNambul
    Authors: Peter Albers, Al Momin
    Subjects: Symplectic Geometry
    Abstract

    We prove that on a restricted contact type hypersurface the number of
    leaf-wise intersections is bounded from below by a certain cup-length.

  4. Rabinowitz Floer homology: A survey.

    Tue, 01/26/2010 - 16:01 — SomNambul
    Authors: Urs Frauenfelder, Peter Albers
    Subjects: Symplectic Geometry
    Abstract

    Rabinowitz Floer homology is the semi-infinite dimensional Morse homology
    associated to the Rabinowitz action functional used in the pioneering work of
    Rabinowitz. Gradient flow lines are solutions of a vortex-like equation. In
    this survey article we describe the construction of Rabinowitz Floer homology
    and its applications to symplectic and contact topology, global Hamiltonian
    perturbations and the study of magnetic fields.

  5. A remark on a Theorem by Ekeland-Hofer.

    Wed, 01/20/2010 - 16:01 — SomNambul
    Authors: Urs Frauenfelder, Peter Albers
    Subjects: Symplectic Geometry
    Abstract

    In [EH89, Theorem 1] Ekeland-Hofer prove that for a centrally symmetric,
    restricted contact type hypersurface in R^{2n} and for any global, centrally
    symmetric Hamiltonian perturbation there exists a leaf-wise intersection point.
    In this note we show that if we replace restricted contact type by star-shaped
    there exists infinitely many leaf-wise intersection points or a leaf-wise
    intersection point on a closed characteristic.

  6. Spectral Invariants in Rabinowitz Floer homology and Global Hamiltonian perturbations.

    Tue, 01/19/2010 - 16:01 — SomNambul
    Authors: Urs Frauenfelder, Peter Albers
    Subjects: Symplectic Geometry
    Abstract

    Spectral invariant were introduced in Hamiltonian Floer homology by Viterbo,
    Oh, and Schwarz. We extend this concept to Rabinowitz Floer homology. As an
    application we derive new quantitative existence results for leaf-wise
    intersections. The importance of spectral invariants for the presented
    application is that spectral invariants allow us to derive existence of
    critical points of the Rabinowitz action functional even in degenerate
    situations where the functional is not Morse.

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