Geodesic
Classification of Morse--Smale diffeomorphisms with one-dimensional set of unstable separatrices
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 62-85

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Let $M^n$ be a closed orientable manifold of dimension $n>3$. We study the class $G_1(M^n)$ of orientation-preserving Morse–Smale diffeomorphisms of $M^n$ such that the set of unstable separatrices of any $f\in G_1(M^n)$ is one-dimensional and does not contain heteroclinic intersections. We prove that the Peixoto graph (equipped with an automorphism) is a complete topological invariant for diffeomorphisms of class $G_1(M^n)$, and construct a standard representative for any class of topologically conjugate diffeomorphisms. 
@article{TM_2010_270_a4,
     author = {V. Z. Grines and E. Ya. Gurevich and V. S. Medvedev},
     title = {Classification of {Morse--Smale} diffeomorphisms with one-dimensional set of unstable separatrices},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {62--85},
     publisher = {mathdoc},
     volume = {270},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_270_a4/}
}
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V. Z. Grines; E. Ya. Gurevich; V. S. Medvedev. Classification of Morse--Smale diffeomorphisms with one-dimensional set of unstable separatrices. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 62-85. http://geodesic.mathdoc.fr/item/TM_2010_270_a4/