N. V. Isaenkova, E. V. Zhuzhoma, L. A. Kuprina, “Solenoidal basic sets of Smale-Vietoris А-diffeomorphisms”, Zhurnal SVMO, 2013, Volume 15, Number 4,Pages <nobr>125

In Middle Volga Mathematical Society

Solenoidal basic sets of Smale-Vietoris А-diffeomorphisms

N. V. Isaenkova^a, E. V. Zhuzhoma^b, L. A. Kuprina^c

^a MIA academy of Nizhnii Novgorod
^b N. I. Lobachevski State University of Nizhni Novgorod
^c Nizhnii Novgorod State Agricultural Academy

Abstract: We introduce Smale-Vietoris diffeomorphisms that include the classical DE-mappings with Smale solenoids. The main result is a correspondence between basic sets of axiom A Smale-Vietoris diffeomorphism and the corresponding nonsingular axiom A endomorphism.

Keywords: hyperbolicity, non-wandering set, nonsingular endomorphism, basic set.

UDC: 517.938