On a classification of axiom A diffeomorphisms with codimension one basic sets and isolated saddles

Let Mⁿ, n 3, be a closed orientable n-manifold and Dₖ (Mⁿ;a, b, c) the set of axiom A diffeomorp\-hisms f: Mⁿ Mⁿ satisfying the following conditions: (1) f has k 1 nontrivial basic sets each is either an orientable codimension one expanding attractor or an orientable codimension one contracting repeller, and other trivial basic sets which are a sinks, b sources, c saddles; (2) the invariant manifolds of isolated saddles are intersected transversally. We classify the diffeomorphisms from Dₖ (Mⁿ;a, b, c) up to the global conjugacy on non-wandering sets for the following subsets Sₖ (Mⁿ;a, b, c), Pₖ (Mⁿ;0, 0, 1), Mₖ (Mⁿ;0, 0, 1) of Dₖ (Mⁿ;a, b, c) where Sₖ (Mⁿ;a, b, c) satisfies to the following conditions: (1ₒ) every nontrivial basic set of any fₖ (Mⁿ;a, b, c) is uniquely bunched, and there is at least one nontrivial attractor and at least one nontrivial repeller, i. e. k 2; (2ₒ) c 1 and all isolated saddles have the same Morse index belonging to \1, n-1\. The subset Pₖ (Mⁿ;0, 0, 1) ₖ (Mⁿ;0, 0, 1) satisfies to the following conditions: (1₏) any boundary point of fₖ (Mⁿ;0, 0, 1) is fixed; (2₏) a unique isolated saddle has Morse index different from \1, n-1\. The subset Mₖ (Mⁿ;0, 0, 1) ₖ (Mⁿ;0, 0, 1) satisfies to the following conditions: (1₌) any boundary point of fₖ (Mⁿ;0, 0, 1) is fixed; (2₌) a unique isolated saddle has Morse index belonging to \1, n-1\. The classification is based on a description of topological structure of supporting manifolds Mⁿ.