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No hyperbolic sets in J∞ for infinitely renormalizable quadratic polynomials

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Abstract

Let f be an infinitely renormalizable quadratic polynomial and J∞ be the intersection of forward orbits of “small” Julia sets of its simple renormalizations. We prove that J∞ contains no hyperbolic sets.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem, 91904, Israel

    Genadi Levin

  2. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich St. 8, 00-956, Warsaw, Poland

    Feliks Przytycki

Authors
  1. Genadi Levin
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  2. Feliks Przytycki
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Correspondence to Genadi Levin.

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Dedicated to Professor Benjamin Weiss on the occasion of his 80th birthday

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Levin, G., Przytycki, F. No hyperbolic sets in J∞ for infinitely renormalizable quadratic polynomials. Isr. J. Math. 251, 635–656 (2022). https://doi.org/10.1007/s11856-022-2443-y

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  • DOI: https://doi.org/10.1007/s11856-022-2443-y

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