Israel Journal of Mathematics

, 108:83

Examples of expandingC1 maps having no σ-finite invariant measure equivalent to Lebesgue


DOI: 10.1007/BF02783043

Cite this article as:
Bruin, H. & Hawkins, J. Israel J. Math. (1998) 108: 83. doi:10.1007/BF02783043


In this paper we construct aC1 expanding circle map with the property that it has no σ-finite invariant measure equivalent to Lebesgue measure. We extend the construction to interval maps and maps on higher dimensional tori and the Riemann sphere. We also discuss recurrence of Lebesgue measure for the family of tent maps.

Copyright information

© Hebrew University 1998

Authors and Affiliations

  1. 1.Department of MathematicsRoyal Institute of TechnologyStockholmSweden
  2. 2.Department of MathematicsUniversity of North Carolina at Chapel HillChapel HillUSA

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