Inventiones mathematicae

, Volume 105, Issue 1, pp 123–136

Invariant measures exist under a summability condition for unimodal maps

  • Tomasz Nowicki
  • Sebastian van Strien

DOI: 10.1007/BF01232258

Cite this article as:
Nowicki, T. & van Strien, S. Invent Math (1991) 105: 123. doi:10.1007/BF01232258


For unimodal maps with negative Schwarzian derivative a sufficient condition for the existence of an invariant measure, absolutely continuous with respect to Lebesgue measure, is given. Namely the derivatives of the iterations of the map in the (unique) critical value must be so large that the sum of (some root of) the inverses is finite.

Copyright information

© Springer International 1991

Authors and Affiliations

  • Tomasz Nowicki
    • 1
  • Sebastian van Strien
    • 2
  1. 1.Mathematics DepartmentWarsaw UniversityPoland
  2. 2.Mathematics DepartmentTU DelftThe Netherlands

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