This article is cited in 1 paper

RESEARCH ARTICLE

Exponent matrices and topological equivalence of maps

Volodymyr Fedorenko^a, Volodymyr Kirichenko^b, Makar Plakhotnyk<sup>b

a</sup> Department of dynamical systems of the Mathematical institute NASU Tereshchenkivska str., 3, Kyiv, Ukraine
^b Department of Mechanics and Mathematics, Kyiv National Taras Shevchenko Univ., Volodymyrska str., 64, 01033 Kyiv, Ukraine

Abstract: Conjugate classes of continuous maps of the interval $[0,\,1]$ into itself, whose iterations form a finite group are described. For each of possible groups of iterations one to one correspondence between conjugate classes of maps and equivalent classes of $(0,\,1)$-exponent matrices of special form is constructed. Easy way of finding the quiver of the map in terms of the set of its extrema is found.

Keywords: exponent matrix, finite orbits, topological equivalence.

MSC: 05С50, 37C15, 37C25

Language: English

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