On a structure of non-wandering set of an $Ω$-stable 3-diffeomorphism possessing a hyperbolic attractor

Marina Barinova, Olga Pochinka, Evgeniy Yakovlev

Published 2023-05-31Version 1

This paper belongs to a series of papers devoted to the study of the structure of the non-wandering set of an A-diffeomorphism. We study such set $NW(f)$ for an $\Omega$-stable diffeomorphism $f$, given on a closed connected 3-manifold $M^3$. Namely, we prove that if all basic sets in $NW(f)$ are trivial except attractors, then every non-trivial attractor is either one-dimensional non-orientable or two-dimensional expanding.