Abstract:
The paper describes the topological structure of closed manifolds of dimension ⩾4 that admit Morse–Smale diffeomorphisms whose nonwandering sets contain arbitrarily many sink periodic points, arbitrarily many source periodic points, and two saddle periodic points. The underlying manifolds of Morse–Smale diffeomorphisms with fewer saddle periodic points are also described.
This work, except for the proof of Theorem 2, was supported
by the Laboratory of Dynamical Systems and Applications at
National Research University Higher School of Economics
(grant of the Ministry of Science and Higher Education of
the Russian Federation, agreement no. 075-15-2019-1931).
The proof of Theorem 2 was supported by the Russian Science
Foundation under grant 17-11-01041.
Citation:
E. V. Zhuzhoma, V. S. Medvedev, “Underlying Manifolds of High-Dimensional Morse–Smale Diffeomorphisms with Two Saddle Periodic Points”, Mat. Zametki, 109:3 (2021), 361–369; Math. Notes, 109:3 (2021), 398–404
This publication is cited in the following 3 articles:
E. V. Zhuzhoma, V. S. Medvedev, “Underlying manifolds of high-dimensional Morse–Smale diffeomorphisms with saddles of codimension 1”, Math. Notes, 116:5 (2024), 1149–1153
V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev, “On Diffeomorphisms with Orientable Codimension 1 Basic Sets and an Isolated Saddle”, Proc. Steklov Inst. Math., 327 (2024), 55–69
E. V. Zhuzhoma, V. S. Medvedev, “Many-Dimensional Morse–Smale Diffeomeophisms with a Dominant Saddle”, Math. Notes, 111:6 (2022), 870–878
Citation in format AMSBIB
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