Acta Mathematica Nitriensia Vol. 1, No. 1, 2015

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Jaroslav Beránek, Jan Chvalina:	Extensions of Cascades Created by Certain Function Systems
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Abstract: Considering three simple function systems which consist of power functions with odd exponents and two linear functions of one real variable, we are constructing actions of the additive group of all integers on the set of all real numbers, i.e. cascades. Using certain extensions based on prolongations of flows, we obtain the system of cascades which are mutually isomorphic. One from consequences of the result is that all solution sets of corresponding functional equations formed with the use of given functions are non-empty, moreover all solution sets consisting of permutations of the set of all reals are non-empty, as well.

Keywords: Mono–unary algebra, orbital decomposition, cascade.

Classification: 26 A 09, 37 B 05

Pages: 50 – 56

DOI: 10.17846/AMN.2015.1.1.50-56

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