ISSN 2079-6900 (Print) 
ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

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MSC2010 37D20, 37G30

Conjugacy of Smale-Vietoris diffeomorphisms using a conjugacy of endomorphisms

N. V. Isaenkova1, E. V. Zhuzhoma2

AnnotationIn the paper, one gets the connection between a conjugacy of Smale-Vietoris diffeomorphisms and corresponding nonsingular circle endomorphisms. To be precise, one gets the necessary condition for a conjugacy of the restriction of Smale-Vietoris diffeomorphism on basic manifolds. One shows that a necessary condition for a conjugacy of the class of diffeomorphisms under consideration is a conjugacy of corresponding circle endomorphisms. In the paper, one proved also the technic theorem which contains some sufficient conditions of the existence of homeomorphism on basic manifolds that takes the orbits of Smale-Vietoris diffeomorphism to the orbits of another diffeomorphism with a commutative diagram of mappings. Together with the first result, one gives the particular solution of the task of the topological equivalence. Later on, the results of this paper can be needed to get invariants of conjugacy of diffeomorphisms of the class under consideration on basic manifolds.
Keywordsconjugacy, commutative diagram, topological equivalence, solenoid, nonsingular endomorphism

1Nataliya V. Isaenkova, Professor of department of Mathematics, Computer Science and Information Technology, Nizhniy Novgorod Academy of the Ministry of the Interior of the Russian Federation  (3 Ankudinovskoe Shosse, Nizhni Novgorod, 603950, Russia), Ph.D. (Physics and Mathematics), ORCID: http://,

2Evgeny V. Zhuzhoma, Professor of department of Fundamental Mathematics, National research University "Higher school of Economics"  ( 25/12 Bolshaya Pecherskaya, Nizhni Novgorod, 603005, Russia), Dr. Sci. (Physics and Mathematics), ORCID:,

Citation: N. V. Isaenkova, E. V. Zhuzhoma , "[Conjugacy of Smale-Vietoris diffeomorphisms using a conjugacy of endomorphisms]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,19:1 (2017) 38–50 (In Russian)

DOI 10.15507/2079-6900.19.2017.01.38-50