Geodesic
Many-Dimensional Morse--Smale Diffeomeophisms with a Dominant Saddle
Matematičeskie zametki, Tome 111 (2022) no. 6, pp. 835-845

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The article defines a class of Morse–Smale diffeomorphisms with a dominant saddle and provides necessary and sufficient conjugacy conditions for such diffeomorphisms. We show that the polar Morse–Smale diffeomorphisms of the $n$-dimensional sphere $\mathbb S^n$, $n\ge4$, whose nonwandering set consists of four points have dominant saddles. As a corollary, we obtain necessary and sufficient conjugacy conditions for such diffeomorphisms. We give examples of polar Morse–Smale diffeomorphisms $\mathbb S^n\to\mathbb S^n$ with such a nonwandering set.
Keywords: Morse–Smale diffeomorphism, dominant saddle.
Mots-clés : conjugacy 
@article{MZM_2022_111_6_a2,
     author = {E. V. Zhuzhoma and V. S. Medvedev},
     title = {Many-Dimensional {Morse--Smale} {Diffeomeophisms} with a {Dominant} {Saddle}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {835--845},
     publisher = {mathdoc},
     volume = {111},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_6_a2/}
}
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E. V. Zhuzhoma; V. S. Medvedev. Many-Dimensional Morse--Smale Diffeomeophisms with a Dominant Saddle. Matematičeskie zametki, Tome 111 (2022) no. 6, pp. 835-845. http://geodesic.mathdoc.fr/item/MZM_2022_111_6_a2/