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On topological classification of Morse–Smale diffeomorphisms on the sphere Sn (n > 3).
- Source :
-
Nonlinearity . Dec2020, Vol. 33 Issue 12, p1-26. 26p. - Publication Year :
- 2020
-
Abstract
- We consider the class G(Sn) of orientation preserving Morse–Smale diffeomorphisms of the sphere Sn of dimension n > 3, assuming that invariant manifolds of different saddle periodic points have no intersection. For any diffeomorphism f ∈ G(Sn), we define a coloured graph Γf that describes a mutual arrangement of invariant manifolds of saddle periodic points of the diffeomorphism f. We enrich the graph Γf by an automorphism Pf induced by dynamics of f and define the isomorphism notion between two coloured graphs. The aim of the paper is to show that two diffeomorphisms f, f′ ∈ G(Sn) are topologically conjugated if and only if the graphs Γf, Γf′ are isomorphic. Moreover, we establish the existence of a linear-time algorithm to distinguish coloured graphs of diffeomorphisms from the class G(Sn). [ABSTRACT FROM AUTHOR]
- Subjects :
- *DIFFEOMORPHISMS
*INVARIANT manifolds
*ALGORITHMS
*SPHERES
*CLASSIFICATION
Subjects
Details
- Language :
- English
- ISSN :
- 09517715
- Volume :
- 33
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Nonlinearity
- Publication Type :
- Academic Journal
- Accession number :
- 147013354
- Full Text :
- https://doi.org/10.1088/1361-6544/abaf60