HYPERBOLIC FIXED POINTS AND PERIODIC ORBITS OF HAMILTONIAN DIFFEOMORPHISMS

    Authors

    V. L. Ginzburg;B. Z. Gurel

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Duke Math. J.

    Keywords

    SYMPLECTIC-MANIFOLDS; CONLEY CONJECTURE; FLOER HOMOLOGY; INDEX; HOMEOMORPHISMS; Mathematics

    Abstract

    We prove that, for a certain class of closed monotone symplectic manifolds, any Hamiltonian diffeomorphism with a hyperbolic fixed point must necessarily have infinitely many periodic orbits. Among the manifolds in this class are complex projective spaces, some Grassmannians, and also certain product manifolds such as the product of a projective space with a symplectically aspherical manifold of low dimension. A key to the proof of this theorem is the fact that the energy required for a Floer connecting trajectory to approach an iterated hyperbolic orbit and cross its fixed neighborhood is bounded away from zero by a constant independent of the order of iteration. This result, combined with certain properties of the quantum product specific to the above class of manifolds, implies the existence of infinitely many periodic orbits.

    Journal Title

    Duke Mathematical Journal

    Volume

    163

    Issue/Number

    3

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    565

    Last Page

    590

    WOS Identifier

    WOS:000331508000004

    ISSN

    0012-7094

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