Topological conjugate piecewise linear unimodal mappings of an interval into itself

  • V. V. Kirichenko
  • M. V. Plakhotnyk Київ. нац. ун-т iм. Т. Шевченка


Let $f, g : [0, 1] \rightarrow [0, 1]$ be a pair of continuous piecewise linear unimodal mappings and let $f$ be defined as follows: $f(x) = 2x$ for $x \leq 1/2$ and $f(x) = 2 - 2x$ for $x > 1/2$. Also let $h : [0, 1] \rightarrow [0, 1]$ be a piecewise differentiable homeomorphism such that $fh = hg$. Then $h$ is piecewise linear and the mapping $f$ completely determines $g$ and $h$, together with the ascending or descending monotone parts of $g$.
How to Cite
Kirichenko, V. V., and M. V. Plakhotnyk. “Topological Conjugate Piecewise Linear Unimodal mappings of an Interval into Itself”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 2, Feb. 2016, pp. 217-26,
Research articles