On semiconjugacy of Williams endomorphism and nonsingular circle endomorphism

N. Isaenkova1, E. Zhuzhoma2, G. Osipov3

AnnotationIn 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.
Keywordssemiconjugacy, one-dimensional branched manifold, non-wandering set, nonsingular endomorphism, basic set

1University professor of department of Mathematics, Computer Science and Information Technology, MIA academy of Nizhnii Novgorod;,

2Professor of department of Fundamental Mathematics, National research University <>, Nizhny Novgorod;

3Professor of Chair of Theory of Control and Dynamics of Machines, Lobachevskii State University, Nizhny Novgorod;

Citation: N. Isaenkova, E. Zhuzhoma, G. Osipov, "[On semiconjugacy of Williams endomorphism and nonsingular circle endomorphism]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,17:4 (2015) 24–30 (In Russian)