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: (1S) 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; (2S) 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: (1P) any boundary point of fₖ(Mⁿ;0,0,1) is fixed; (2P) 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: (1M) any boundary point of fₖ(Mⁿ;0,0,1) is fixed; (2M) 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.