Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere
- We construct a dynamically convex contact form on the three-sphere whose systolic ratio is arbitrarily close to 2. This example is related to a conjecture of Viterbo, whose validity would imply that the systolic ratio of a convex contact form does not exceed 1. We also construct, for every integer \(\textbf {n ≥ 2}\), a tight contact form with systolic ratio arbitrarily close to \(\it n\) and with suitable bounds on the mean rotation number of all the closed orbits of the induced Reeb flow.
| Author: | Alberto AbbondandoloGND, Barney BramhamGND, Umberto L. HryniewiczGND, Pedro A. S. SalomãoGND |
|---|---|
| URN: | urn:nbn:de:hbz:294-69060 |
| DOI: | https://doi.org/10.1112/S0010437X18007558 |
| Parent Title (English): | Compositio mathematica |
| Publisher: | Cambridge University Press |
| Place of publication: | Cambridge |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2020/01/22 |
| Date of first Publication: | 2018/11/06 |
| Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
| Tag: | Finite-dimensional Hamiltonian and nonholonomic systems; Lagrangian; contact; nonholonomic systems |
| Volume: | 154 |
| Issue: | 12 |
| First Page: | 2643 |
| Last Page: | 2680 |
| Note: | © Copyright Cambridge University Press. Permission for reuse must be granted by Cambridge University Press in the first instance. |
| Institutes/Facilities: | Lehrstuhl VII - Analysis |
| open_access (DINI-Set): | open_access |
| faculties: | Fakultät für Mathematik |
| Licence (German): |  Nationale Lizenz |
