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On the conjugation of some class of one-dimensional endomorphisms with a class of piecewise expanding mappings. (English. Russian original) Zbl 0605.28016
Russ. Math. Surv. 40, No. 1, 211-212 (1985); translation from Usp. Mat. Nauk 40, No. 1(241), 187-188 (1985).
Let T be a piecewise continuously differentiable mapping of an interval \([a,b]\) into itself. The author gives conditions under which there is a non-singular conjugation of T with a piecewise expanding mapping. The results are then applied to the family of mappings \(T_ ax=ax(1-x)\) of the unit interval into itself. It is shown that there is a continuum of values of the parameter a for which \(T_ a\) is non-singularly conjugate to a piecewise expanding mapping.
Reviewer: D.Newton

MSC:
28D99 Measure-theoretic ergodic theory
37A99 Ergodic theory
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