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

N. V. Isaenkova ; E. V. Zhuzhoma

Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 3, pp. 295-310.

Résumé

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.

Détail

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

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