| Title:
|
Non equivalence of NMS flows on $S^{3}$ (English) |
| Author:
|
Campos, B. |
| Author:
|
Vindel, P. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
137 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
165-173 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We build the flows of non singular Morse-Smale systems on the 3-sphere from its round handle decomposition. We show the existence of flows corresponding to the same link of periodic orbits that are non equivalent. So, the link of periodic orbits is not in a 1-1 correspondence with this type of flows and we search for other topological invariants such as the associated dual graph. (English) |
| Keyword:
|
non singular Morse-Smale flows |
| Keyword:
|
round handle decomposition |
| Keyword:
|
link |
| MSC:
|
37D15 |
| MSC:
|
57M25 |
| idZBL:
|
Zbl 1265.37008 |
| idMR:
|
MR2978262 |
| DOI:
|
10.21136/MB.2012.142862 |
| . |
| Date available:
|
2012-06-08T10:09:29Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142862 |
| . |
| Reference:
|
[1] Asimov, D.: Round handles and non-singular Morse-Smale flows.Ann. Math. 102 (1975), 41-54. Zbl 0316.57020, MR 0380883, 10.2307/1970972 |
| Reference:
|
[2] Campos, B., Martínez Alfaro, J., Vindel, P.: Bifurcations of links of periodic orbits in non-singular Morse-Smale systems on $S^{3}$.Nonlinearity 10 (1997), 1339-1355. MR 1473388, 10.1088/0951-7715/10/5/018 |
| Reference:
|
[3] Campos, B., Martínez Alfaro, J., Vindel, P.: Graphs of NMS flows on $S^{3}$ with unknotted saddle periodic orbits.Topol. Proc. 26 (2001-2002), 469-483. MR 2032833 |
| Reference:
|
[4] Campos, B., Vindel, P.: Graphs of NMS flows on $ S^{3} $ with knotted saddle orbits and no heteroclinic trajectories.Acta Math. Sin., Engl. Ser. 23 (2007), 2213-2224. Zbl 1137.37312, MR 2357455, 10.1007/s10114-007-0969-x |
| Reference:
|
[5] Morgan, J. W.: Non-singular Morse-Smale flows on 3-dimensional manifolds.Topology 18 (1978), 41-53. MR 0528235, 10.1016/0040-9383(79)90013-2 |
| Reference:
|
[6] Nikolaev, I., Zhuzhoma, E.: Flows on 2-dimensional Manifolds.Lectures Notes in Mathematics 1705. Springer, Berlin (1999). Zbl 1022.37027, MR 1707298, 10.1007/BFb0093599 |
| Reference:
|
[7] Wada, M.: Closed orbits of non-singular Morse-Smale flows on $S^3$.J. Math. Soc. Japan 41 (1989), 405-413. MR 0999505, 10.2969/jmsj/04130405 |
| Reference:
|
[8] Yano, K.: The homotopy class of non-singular Morse-Smale vector fields on 3-manifolds.Invent. Math. 80 (1985), 435-451. Zbl 0622.58018, MR 0791668, 10.1007/BF01388724 |
| . |
