Communications in Mathematical Physics

, Volume 208, Issue 1, pp 91–105

Rigidity of C2 Infinitely Renormalizable Unimodal Maps

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

DOI: 10.1007/s002200050749

Cite this article as:
de Melo, W. & Pinto, A. Comm Math Phys (1999) 208: 91. doi:10.1007/s002200050749


Given C2 infinitely renormalizable unimodal maps f and g with a quadratic critical point and the same bounded combinatorial type, we prove that they are C1+α conjugate along the closure of the corresponding forward orbits of the critical points, for some α>0.

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