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Singular measures without restrictive intervals

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Abstract

For the transformationT:[0,1]↦[0,1] defined byT(x)=λx(1−x) with 0≦λ≦4, a λ is shown to exist for whichT has no restrictive intervals, hence is sensitive to initial conditions, but for which no finite absolutely continuous invariant measure exists forT.

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Communicated by J. Mather

Supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University

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Johnson, S.D. Singular measures without restrictive intervals. Commun.Math. Phys. 110, 185–190 (1987). https://doi.org/10.1007/BF01207362

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  • DOI: https://doi.org/10.1007/BF01207362

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