On Ω-stable 3-Diffeomorphism with a Solid or Thickened Surfaced Basic Set

In the present paper we consider an ohm-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial basic sets. Also, we have collected few results on expanding attractors that are generally considered well-known but have not been formulated in the literature in a way that allows for direct citation. This concerns the path connected components of such m-dimensional attractors for n-diffeomorphism 1 <= m < n, as well as the topology of trapping neighborhood of one-dimensional expanding attractor of a 3-diffeomorphism. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, Al training, and similar technologies.