Derivative of the conjugacy for the pair of tentlike mappings of interval at rational points (in Ukrainian) |
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| Author |
makar_plakhotnyk@ukr.net
University of Sao Paulo, Brasil
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| 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.
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| Keywords |
conjugacy; tent-like mapping
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| DOI |
doi:10.15330/ms.46.2.196-202
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| Reference |
1. Fedorenko V.V., Plakhotnyk M.V. Topological conjugation of piecewise linear unimodal maps// Collected
articles of Kyiv institute of Mathematics of National Academy of Sciences of Ukraine. - 2014. - V. 11,
¹5. - P. 115-127. (in Ukrainian)
2. Plakhotnyk M. Differentiability of the conjugation for the pair of tent-like maps// Bull. of Kyiv University, Ser. Mathematics and Mechanics. - 2015. - V.34. - P. 28-34. (in Ukrainian) 3. Riesz F., Sz.-Nagy B. Lections on functional analysis. - Mir, Moskow, 1979. (in Russian); also see Riesz F., Sz.-Nagy B. Lecons dAnalyse Fonctionnelle. . Budapest, 1955. (in French) 4. Fihtengoltz G.M. The course of differential and integral calculus. - Nauka, Moscow, 1962. (in Russian) 5. A.N. Sharkovskiy, S.F. Koliada, A.G. Sivak, V.V. Fedorenko, Introduction to the funtional equations theory. - Naukova Dumka, Kyiv, 1989. (in Russian) 6. Fedorenko V., Kyrychenko V., Plakhotnyk M. Exponent matrices and topological equivalence of maps// Algebra and Discrete Math. - 2007. - ¹4. - P. 45-58. 7. Lebesgue H. Lecons sur lintegration et le recherche des fonctions primitives. - 2-me ed., Paris, 1928. 8. Skufca J., Bolt E., A concept of homeomorphic defect for defining mostly conjugate dynamical systems// - 2008. - Chaos. - ¹03118. - P. 1-18. |
| Pages |
196-202
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| Volume |
46
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| Issue |
2
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| Year |
2016
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| Journal |
Matematychni Studii
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| Full text of paper | |
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