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arXiv · 2305.19579

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

Marina Barinova·Olga Pochinka·Evgeniy Yakovlev
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Abstract

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.

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Marina Barinova, Olga Pochinka, Evgeniy Yakovlev. 2023-05-31. On a structure of non-wandering set of an $\Omega$-stable 3-diffeomorphism possessing a hyperbolic attractor. https://arxiv.org/abs/2305.19579

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