Geodesic
On Morse--Smale Diffeomorphisms with Four Periodic Points on Closed Orientable Manifolds
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 369-386

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We study Morse–Smale diffeomorphisms of n-manifolds with four periodic points which are the only periodic points. We prove that for $n= 3$ these diffeomorphisms are gradient-like and define a class of diffeomorphisms inevitably possessing a nonclosed heteroclinic curve. For $n\ge4$, we construct a complete conjugacy invariant in the class of diffeomorphisms with a single saddle of codimension one. 
@article{MZM_2003_74_3_a5,
     author = {V. Z. Grines and E. V. Zhuzhoma and V. S. Medvedev},
     title = {On {Morse--Smale} {Diffeomorphisms} with {Four} {Periodic} {Points} on {Closed} {Orientable} {Manifolds}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {369--386},
     publisher = {mathdoc},
     volume = {74},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a5/}
}
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V. Z. Grines; E. V. Zhuzhoma; V. S. Medvedev. On Morse--Smale Diffeomorphisms with Four Periodic Points on Closed Orientable Manifolds. Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 369-386. http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a5/