Generalized counterexamples to the Seifert conjecture
| dc.creator | Kuperberg, Greg | |
| dc.creator | Kuperberg, Krystyna | |
| dc.date | 1998-02-06 | |
| dc.date.accessioned | 2026-07-07T05:23:48Z | |
| dc.date.available | 2026-07-07T05:23:48Z | |
| dc.description | Using the theory of plugs and the self-insertion construction due to the second author, we prove that a foliation of any codimension of any manifold can be modified in a real analytic or piecewise-linear fashion so that all minimal sets have codimension 1. In particular, the 3-sphere S^3 has a real analytic dynamical system such that all limit sets are 2-dimensional. We also prove that a 1-dimensional foliation of a manifold of dimension at least 3 can be modified in a piecewise-linear fashion so that there are no closed leaves but all minimal sets are 1-dimensional. These theorems provide new counterexamples to the Seifert conjecture, which asserts that every dynamical system on S^3 with no singular points has a periodic trajectory. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/9802040 | |
| dc.identifier | http://arxiv.org/abs/math/9802040 | |
| dc.identifier | Ann. of Math. (2) 144 (1996), 239--268 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76586 | |
| dc.subject | Dynamical Systems | |
| dc.title | Generalized counterexamples to the Seifert conjecture | |
| dc.type | text |