Piecewise convex transformations with no finite invariant measure

Volume 54 / 1991

Tomasz Komorowski Annales Polonici Mathematici 54 (1991), 59-68 DOI: 10.4064/ap-54-1-59-68


 Abstract. The paper concerns the problem of the existence of a finite invariant absolutely continuous measure for piecewise $C^2$-regular and convex transformations T: [0, l]→[0,1]. We show that in the case when T'(0) = 1 and T"(0) exists T does not admit such a measure. This result is complementary to the ones contained in [3] and [5].


  • Tomasz Komorowski

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