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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
H. Lebesgue, Le¸cons sur l’Intêgration et la Recherche des Fonctions Primitives, Gauthier-Villars, Paris (1928).
F. C. Moon, Chaotic Vibrations. An Introduction for Applied Scientists and Engineers, Wiley, New York (1997).
A. Poincaré, Selected Works. New Methods of Celestial Mechanics [in Russian], Vol. 1, Nauka, Moscow (1971).
F. Riesz and B. S.-Nagy, Lecons D’Analyse Fonctionnelle [Russian translation], Mir, Moscow (1979).
A. N. Sharkovskii, S. F. Kolyada, A. G. Sivak, and V. V. Fedorenko, Introduction to the Theory of Functional Equations [in Russian], Naukova Dumka, Kiev (1989).
V. Fedorenko, V. Kyrychenko, and M. Plakhotnyk, “Exponent matrices and topological equivalence of maps,” Algebra Discrete Math., No. 4, 45–58 (2007).
J. D. Skufca and E. M. Bolt, “A concept of homeomorphic defect for defining mostly conjugate dynamical systems,” Chaos, No. 03118, 1–18 (2008).
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 2, pp. 217–226, February, 2016.
About this article
Cite this article
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