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Topological Conjugate Piecewise Linear Unimodal Mappings of an Interval Into Itself

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Let f, g : [0, 1] → [0, 1] be a pair of continuous piecewise linear unimodal mappings and let f be defined as follows: f(x) = 2x for x ≤ 1/2 and f(x) = 2 − 2x for x > 1/2. Also let h : [0, 1] → [0, 1] be a piecewise continuously differentiable homeomorphism such that fh = hg. Then h is piecewise linear and the mapping f, together with the ascending (or descending) monotone part of g, completely determines g and h.

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Correspondence to V. V. Kyrychenko.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 2, pp. 217–226, February, 2016.

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Kyrychenko, V.V., Plakhotnyk, M.V. Topological Conjugate Piecewise Linear Unimodal Mappings of an Interval Into Itself. Ukr Math J 68, 242–252 (2016). https://doi.org/10.1007/s11253-016-1221-6

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