Singular measures without restrictive intervals |
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Authors: | Stewart D. Johnson |
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Affiliation: | (1) Department of Mathematics, Cornell University, 14850 Ithaca, NY, USA |
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Abstract: | For the transformationT:[0,1] [0,1] defined byT(x)= x(1–x) with 0![lE](/content/j866644755l0jj40/xxlarge8806.gif) ![lambda](/content/j866644755l0jj40/xxlarge955.gif) 4, a 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.Supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University |
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