Abstract
We consider the class \(\mathbb{G}_k^{\text{diff}}(M^n;0,0,1)\) of diffeomorphisms \(f \colon\, M^n\to M^n\) of a closed orientable \(n\) -manifold \(M^n\) , \(n\geq 3\) , that satisfy Smale’s axiom A whose nonwandering set \(\mathrm{NW}(f)\) consists of the following basic sets: (a) \(k\geq 1\) nontrivial basic sets each of which is either an orientable connected expanding codimension \(1\) attractor or an orientable connected contracting codimension \(1\) repeller; (b) exactly one trivial basic set, an isolated saddle, whose separatrices do not intersect. For diffeomorphisms in \(\mathbb{G}_k^{\text{diff}}(M^n;0,0,1)\) , we construct a certain equipped graph that gives a complete global conjugacy invariant on their nonwandering sets. We also describe the topological structure of the supporting manifolds \(M^n\) for diffeomorphisms in the class \(\mathbb{G}_k^{\text{diff}}(M^n;0,0,1)\) , \(n\geq 3\) , \(n\neq 4\) , \(k\geq 2\) .
