Piecewise convex transformations with no finite invariant measure

Tomasz Komorowski

ArticleOriginal scientific text

Title

Piecewise convex transformations with no finite invariant measure

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Affiliations

Institute of Mathematics, M. Curie-Skłodowska University, Pl. M. Curie-Skłodowskicj I, 20-031 Lublin, Poland

Abstract

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].

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Title

Piecewise convex transformations with no finite invariant measure

Affiliations

Abstract

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