Communications in Mathematical Physics

, Volume 208, Issue 1, pp 91–105 | Cite as

Rigidity of C 2 Infinitely Renormalizable Unimodal Maps

  • W. de Melo
  • A. A.  Pinto
Original article


Given C 2 infinitely renormalizable unimodal maps f and g with a quadratic critical point and the same bounded combinatorial type, we prove that they are C 1+α conjugate along the closure of the corresponding forward orbits of the critical points, for some α>0.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • W. de Melo
    • 1
  • A. A.  Pinto
    • 2
  1. 1.IMPA, Rio de Janeiro, Brazil. E-mail: demelo@impa.brBR
  2. 2.DMA, Faculdade de Ciências, Universidade do Porto, 4000 Porto, Portugal. E-mail: aapinto@fc.up.ptPT

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