Classification of Meromorphic Vector Fields

    Project Details

    Description

    A complex polynomial defines a holomorphic vector field in the complex
    plane. The quasi-conformal conjugacy class of the polynomial is completely
    determined by a combinatorial invariant. Furthermore, within each
    combinatorial class the polynomial is uniquely determined by a finite number
    (settled by the combinatorial class) of complex numbers. This fundamental
    classification of complex polynomial vector fields is proved using surgery.

    Further developments are to classify possible bifurcations, to understand
    the decomposition of parameter spaces due to the different combinatorial classes
    and the bifurcations among them, and also to extend to meromorphic vector
    fields arising from rational functions on the Riemann sphere.
    StatusFinished
    Effective start/end date01/09/200631/08/2009

    Keywords

    • Holomorphic Dynamical Systems