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Giulio Tiozzo

  1. The entropy of alpha-continued fractions: analytical results.

    Втр, 12/15/2009 - 16:01 — SomNambul
    Authors: Giulio Tiozzo
    Subjects: Dynamical Systems
    Abstract

    We study the ergodic theory of a one-parameter family of interval maps
    arising from generalized continued fraction algorithms. First of all, we prove
    a central limit theorem for bounded variation observables and for the metric
    entropy. Moreover, we discuss the stability of the spectral decomposition of
    the Ruelle-Perron-Frobenius operator as the parameter alpha varies.

  2. The entropy of alpha-continued fractions: numerical results.

    Пнд, 12/14/2009 - 16:01 — SomNambul
    Authors: Carlo Carminati, Stefano Marmi, Alessandro Profeti, Giulio Tiozzo
    Subjects: Dynamical Systems
    Abstract

    We consider the one-parameter family of interval maps arising from
    generalized continued fraction expansions known as alpha-continued fractions.
    For such maps, we perform a numerical study of the behaviour of metric entropy
    as a function of the parameter. The behaviour of entropy is known to be quite
    regular for parameters for which a matching condition on the orbits of the
    endpoints holds.

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