Israel Journal of Mathematics

, 108:83 | Cite as

Examples of expandingC 1 maps having no σ-finite invariant measure equivalent to Lebesgue

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Abstract

In this paper we construct aC 1 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.

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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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