N. V. Isaenkova, E. V. Zhuzhoma, G. V. Osipov, “On semiconjugacy of Williams endomorphism and nonsingular circle endomorphism”, Zhurnal SVMO, 2015, Volume 17, Number 4,Pages <nobr>24

Mathematics

On semiconjugacy of Williams endomorphism and nonsingular circle endomorphism

N. V. Isaenkova^a, E. V. Zhuzhoma^b, G. V. Osipov^c

^a MIA academy of Nizhnii Novgorod
^b Institute for Statistical Studies and Economics of Knowledge, National Research University "Higher School of Economics"
^c Institute of Informational Technologies, Mathematics and Mechanics, Lobachevsky State University of Nizhny Novgorod

Abstract: In the paper, we proof that Williams endomorphism of one-dimensional branched manifold with two branched points semiconjugates with the nonsingular circle endomorphism of degree three. As a consequence, one gets that the non-wandering set of the Williams endomorphism contains Cantor set.

Keywords: semiconjugacy, one-dimensional branched manifold, non-wandering set, nonsingular endomorphism, basic set.

UDC: 517.9+519.8

Received: 11.12.2015