Geodesic
On the compliance of the basic sets of A-endomorphisms and A-diffeomorphisms
Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 3, pp. 295-310

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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. 
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     author = {N. V. Isaenkova and E. V. Zhuzhoma},
     title = {On the compliance of the basic sets of {A-endomorphisms} and {A-diffeomorphisms}},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {295--310},
     publisher = {mathdoc},
     volume = {3},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a2/}
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N. V. Isaenkova; E. V. Zhuzhoma. On the compliance of the basic sets of A-endomorphisms and A-diffeomorphisms. Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 3, pp. 295-310. http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a2/