Publication details
Extensions of Cascades Created by Certain Function Systems
| Authors | |
|---|---|
| Year of publication | 2015 |
| Type | Article in Periodical |
| Magazine / Source | Acta Mathematica Nitriensia |
| MU Faculty or unit | |
| Citation | |
| Field | Pedagogy and education |
| Keywords | mono-unary algebra; orbital decomposition; cascade |
| Description | The article was created on the basis of scientific research in the area of interdisciplinary relations between algebra and mathematical analysis with the aim to find deeper connections between these two branches.Considering three simple function systems which consists 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. |