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
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.
solenoid, axiom A, basic set, bifurcation.
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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
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\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.
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