A Hölder continuous vector field tangent to many foliations
| dc.creator | Bonatti, Christian | |
| dc.creator | Franks, John | |
| dc.date | 2003-03-24 | |
| dc.date.accessioned | 2026-07-07T04:56:19Z | |
| dc.date.available | 2026-07-07T04:56:19Z | |
| dc.description | We construct an example of a Hölder continuous vector field on the plane which is tangent to all foliations in a continuous family of pairwise distinct $C^1$ foliations. Given any $1 \le r <\infty,$ the construction can be done in such a way that each leaf of each foliation is the graph of a $C^r$ function from $\R$ to $\R.$ We also show the existence of a continuous vector field $X$ on $\R^2$ and two foliations $\cal{F}$ and $\cal{G}$ on $\R^2$ each tangent to $X$ with a dense subset $\cal E$ of $\R^2$ such that at every point $x\in \cal E$ the leaves $F_x$ and $G_x$ of the foliation $\cal{F}$ and $\cal{G}$ through $x$ are topologically transverse. | |
| dc.identifier | https://arxiv.org/abs/math/0303291 | |
| dc.identifier | http://arxiv.org/abs/math/0303291 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66876 | |
| dc.subject | Dynamical Systems | |
| dc.title | A Hölder continuous vector field tangent to many foliations | |
| dc.type | text |