Genus zero transverse foliations for weakly convex Reeb flows on the tight $3$-sphere
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911994720813056 |
|---|---|
| author | de Paulo, Naiara V. Hryniewicz, Umberto Kim, Seongchan Salomão, Pedro A. S. |
| author_facet | de Paulo, Naiara V. Hryniewicz, Umberto Kim, Seongchan Salomão, Pedro A. S. |
| contents | A contact form on the tight $3$-sphere $(S^3,ξ_0)$ is called weakly convex if the Conley-Zehnder index of every Reeb orbit is at least $2$. In this article, we study Reeb flows of weakly convex contact forms on $(S^3,ξ_0)$ admitting a prescribed finite set of index-$2$ Reeb orbits, which are all hyperbolic and mutually unlinked. We present conditions so that these index-$2$ orbits are binding orbits of a genus zero transverse foliation whose additional binding orbits have index $3$. In addition, we show in the real-analytic case that the topological entropy of the Reeb flow is positive if the branches of the stable/unstable manifolds of the index-$2$ orbits are mutually non-coincident. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12856 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Genus zero transverse foliations for weakly convex Reeb flows on the tight $3$-sphere de Paulo, Naiara V. Hryniewicz, Umberto Kim, Seongchan Salomão, Pedro A. S. Symplectic Geometry Dynamical Systems A contact form on the tight $3$-sphere $(S^3,ξ_0)$ is called weakly convex if the Conley-Zehnder index of every Reeb orbit is at least $2$. In this article, we study Reeb flows of weakly convex contact forms on $(S^3,ξ_0)$ admitting a prescribed finite set of index-$2$ Reeb orbits, which are all hyperbolic and mutually unlinked. We present conditions so that these index-$2$ orbits are binding orbits of a genus zero transverse foliation whose additional binding orbits have index $3$. In addition, we show in the real-analytic case that the topological entropy of the Reeb flow is positive if the branches of the stable/unstable manifolds of the index-$2$ orbits are mutually non-coincident. |
| title | Genus zero transverse foliations for weakly convex Reeb flows on the tight $3$-sphere |
| topic | Symplectic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2206.12856 |