Institut de Mathématiques de Toulouse

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  • Systèmes Dynamiques

    Vendredi 12 mai 2017 10:30-11:30 - Giulio Tiozzo

    The core entropy for polynomials of higher degree

    Résumé : The notion of topological entropy for real multimodal maps goes back to the
    work of Milnor and Thurston in the 1970s. In order to extend this definition from the world of real maps to complex polynomials, W. Thurston defined a few years ago the notion of core entropy as the entropy of the restriction of the polynomial to its underlying Hubbard tree.
    In this talk, I will discuss the notion of core entropy and their definition for polynomials of any degree. In particular, we will explore the space PM(d) of "primitive majors" which serves as a combinatorial model for the space of polynomials of degree d, see how to compute the core entropy from the combinatorial data and prove it varies continuously on the parameter space.
    This is joint work with Gao Yan.

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