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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
##### Keywords:
non-singular conjugation; piecewise expanding mapping
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