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UID:node-3133868@mathematics.huji.ac.il
DTSTAMP:20221129T120000Z
DTSTART:20221129T120000Z
DTEND:20221129T130000Z
SUMMARY:Dynamics seminar: Genady Levin (HUJI) On renormalizations of rational functions
DESCRIPTION:*Abstract:*We recall Douady-Hubbard's polynomial-like renormalization \n("satellite" and "primitive"), Sullivan's "complex bounds", Douady-Hubbard's \nexamples of "no complex bounds" etc., and review some related phenomena and \nadvances.\nThen we discuss two recent results. The first one is a universal drop of \ncomplex bounds at a satellite renormalizationof high relative period. This \nimplies, e.g., no complex bounds for all "satellite" maps of unbounded \ncombinatorics\n(extending Douady-Hubbard's examples), and degeneration of geometry in this \ncase.\nIn the second result, we consider the dynamics of a quadratic polynomial \nwhich admits infinitely many satellite renormalizations.\nThe mostinteresting case is when the "intersection" J_\infty of all \nrenormalizations contains continua. We show that any invariant measure on \nJ_\infty is,\nin fact, supported on the postcritical set and has zero Lyapunov exponent. It \nfollows that the exponent at the critical value is equal to zero, too.\nJoint works with Alexander B...
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