Abstract
We consider periodic components of A-diffeomorphisms on two-dimensional manifolds. We study properties of these components and give a topological description of their boundaries.
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REFERENCES
G. Birkhoff and P. Smith, “Structure analysis of surface transformations,” J. Math., 7, 357–369 (1928).
P. Smith, “The regular components of surface transformations,” Amer J. Math., 52, No. 2, 357–369 (1930).
S. H. Aranson and V. S. Medvedev, “Regular components of homeomorphisms of an n-dimensional sphere,” Mat. Sb., 85, No. 1, 3–17 (1971).
J. Palis and V. de Melo, Geometric Theory of Dynamical Systems [Russian translation], Mir, Moscow (1986).
S. Smale, “Differentiable dynamical systems,” Bull. Amer. Math. Soc., 73, 747–792 (1967).
A. Bezen, “On the topological properties and the topological conjugacy of two-dimensional Morse-Smale diffeomorphisms,” Rand. Comput. Dynamics, 2, No. 2, 183–203 (1994).
R. V. Plykin, “On geometry of hyperbolic attractors,” Mat. Zametki, 39, No. 6, 75–113 (1984).
R. V. Plykin, “Sources and sinks of A-diffeomorphisms of surfaces,” Mat. Sb, 94, No. 2, 243–264 (1974).
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Vlasenko, I.Y. Topological Properties of Periodic Components of A-Diffeomorphisms. Ukrainian Mathematical Journal 54, 1239–1250 (2002). https://doi.org/10.1023/A:1023460021749
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DOI: https://doi.org/10.1023/A:1023460021749