Topology of the regular part for infinitely renormalizable quadratic polynomials

Volume 208 / 2010

Carlos Cabrera, Tomoki Kawahira Fundamenta Mathematicae 208 (2010), 35-56 MSC: 37F10, 37F25, 37F45. DOI: 10.4064/fm208-1-3


We describe the well studied process of renormalization of quadratic polynomials from the point of view of their natural extensions. In particular, we describe the topology of the inverse limit of infinitely renormalizable quadratic polynomials and prove that when they satisfy a priori bounds, the topology is rigid modulo combinatorial equivalence.


  • Carlos CabreraInstituto de Matemáticas
    Unidad Cuernavaca, UNAM
    Av. Universidad s//n, Col. Lomas de Chamilpa
    C. P. 62210, Cuernavaca, Morelos, Mexico
  • Tomoki KawahiraGraduate School of Mathematics
    Nagoya University
    Nagoya 464-8602, Japan

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