Nathaniel D. Emerson

  1. On Yoccoz Return Functions.

    Authors: Nathaniel D. Emerson
    Subjects: Dynamical Systems
    Abstract

    We study the dynamics of complex polynomials. We obtain results on Poincare
    return maps defined on certain neighborhoods of a point with bounded orbit
    under a polynomial. We introduce a generalization of the Yoccoz tau-function,
    the Yoccoz return function, which codes the returns of a critical point with
    bounded orbit of any complex polynomial with a disconnect Julia set. We give
    necessary conditions on Yoccoz return functions, which allow for the recursive
    definition of an abstract tau-function.

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