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Organizers |
Graphs of NMS Flows on S3
by
Pura Vindel
Dpt. Matemáticas. Campus de Riu Sec. ESTCE. Universitat de Castellón. Spain
Coauthors: B. Campos, J. Martínez Alfaro
Morse-Smale flows form a dense open subset of C\infty-vector fields and they are structurally stable flows on 2-dimensional manifolds. For the three dimensional case, they are not dense, but they define an open set in the set of C1-vector fields; in most cases they can be studied from non-singular Morse-Smale flows, that are characterized by the following features:
- There are a finite number of hyperbolic periodic orbits.
- No trajectory connects saddle periodic orbits.
- Each of the limit sets of every trajectory is a closed orbit.
For the case of NMS flows on the 3-sphere a topological characterization of the set of the periodic orbits has been made by M. Wada in terms of knots and links, using a generator, the Hopf link, and six operations. The Hopf link consists of two linked trivial knots corresponding to one attractive and one repulsive periodic orbit; the six operations are basically split sums and cabling.
X. Wang obtains a complete classification of the C*-algebras of all Morse-Smale flows on closed 2-manifolds in terms of dual graphs, showing that the coloured dual graphs are exactly the complete combinatorial invariant of the topological conjugacy classes of the Morse-Smale flows on closed 2-manifolds.
Our aim is to obtain the dual graphs associated to the NMS systems on S3 corresponding to Wada operations applied on Hopf links from the global picture of the corresponding flow.
Date received: May 21, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagw-71.