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Alexandre Eremenko

  1. Dynamics of a higher dimensional analog of the trigonometric functions.

    Tue, 02/23/2010 - 16:01 — SomNambul
    Authors: Walter Bergweiler, Alexandre Eremenko
    Subjects: Dynamical Systems
    Abstract

    We introduce a higher dimensional quasiregular map analogous to the
    trigonometric functions and we use the dynamics of this map to define, for d>1,
    a partition of d-dimensional Euclidean space into curves tending to infinity
    such that two curves may intersect only in their endpoints and such that the
    union of the curves without their endpoints has Hausdorff dimension one.

  2. On the number of solutions of a transcendental equation arising in the theory of gravitational lensing.

    Tue, 09/01/2009 - 12:47 — SomNambul
    Authors: Walter Bergweiler, Alexandre Eremenko
    Subjects: Complex Variables
    Abstract

    The equation in the title describes the number of bright images of a point
    source under lensing by an elliptic object with isothermal density. We prove
    that this equation has at most 6 solutions. Any number of solutions from 1 to 6
    can actually occur.

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