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Chelyab. Fiz.-Mat. Zh., 2018, Volume 3, Issue 3, Pages 295–310 (Mi chfmj106)  

Mathematics

On the compliance of the basic sets of A-endomorphisms and A-diffeomorphisms

N. V. Isaenkovaa, E. V. Zhuzhomab

a Nizhniy Novgorod Academy of the Ministry of Internal Affairs of the Russian Federation, Nizhniy Novgorod, Russia
b National research University "Higher school of Economics", Nizhniy Novgorod, Russia

Abstract: We consider a class of Smale — Vietoris A-diffeomorphisms that are defined using basic A-endomorphisms of manifolds, the dimension of which is less than the dimension of the supporting manifolds of A-diffeomorphisms. The class of Smale — Vietoris diffeomorphisms contains DE-mappings of Smale. We show that there is a one-to-one correspondence between the basic sets of the basic A-endomorphism and Smale — Vietoris diffeomorphisms. For back-invariant basic set of basis A-endomorphism there is an accurate description of the corresponding non-trivial basic set of Smale — Vietoris A-diffeomorphism. Using the description obtained, one constructs the bifurcation between different types of solenoidal basic sets.

Keywords: solenoid, axiom A, basic set, bifurcation.

Funding Agency Grant Number
Russian Science Foundation 17-11-01041
HSE Basic Research Program -95


DOI: https://doi.org/10.24411/2500-0101-2018-13303

Full text: PDF file (742 kB)
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Received: 21.06.2018
Revised: 21.07.2018

Citation: N. V. Isaenkova, E. V. Zhuzhoma, “On the compliance of the basic sets of A-endomorphisms and A-diffeomorphisms”, Chelyab. Fiz.-Mat. Zh., 3:3 (2018), 295–310

Citation in format AMSBIB
\Bibitem{IsaZhu18}
\by N.~V.~Isaenkova, E.~V.~Zhuzhoma
\paper On the compliance of the basic sets of A-endomorphisms and A-diffeomorphisms
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2018
\vol 3
\issue 3
\pages 295--310
\mathnet{http://mi.mathnet.ru/chfmj106}
\crossref{https://doi.org/10.24411/2500-0101-2018-13303}
\elib{http://elibrary.ru/item.asp?id=35559233}


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