Derivative of the conjugacy for the pair of tentlike mappings of interval at rational points (in Ukrainian)

Author
M. V. Plakhotnyk
University of Sao Paulo, Brasil
Abstract
It is studied the conjugacy $h=h_v$, for the tent-like mappings $f_{1/2}$ and $f_v\colon [0,\, 1]\rightarrow [0,\, 1]$, $v\in (0,\, 1)$, where the function $f_v$ is linear at each of intervals $[0,\, v]$ and $[v,\ 1]$, $f_v(0)=f_v(1)=0$, $f_v(v)=1$, i.e. we consider the homeomorphism $h\colon [0,\, 1]\rightarrow [0,\ 1]$ such that $h\circ f = f_v\circ h$. We prove the differentiability of $h$ at all rational points.
Keywords
conjugacy; tent-like mapping
DOI
doi:10.15330/ms.46.2.196-202
Reference
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Pages
196-202
Volume
46
Issue
2
Year
2016
Journal
Matematychni Studii
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