Many-Dimensional Morse--Smale Diffeomeophisms with a Dominant Saddle

E. V. Zhuzhoma ; V. S. Medvedev

Matematičeskie zametki, Tome 111 (2022) no. 6, pp. 835-845.

Résumé

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.

Détail

Keywords: Morse–Smale diffeomorphism, dominant saddle.
Mots-clés : conjugacy

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