## On the structure of Besse convex contact spheres

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Marco Mazzucchelli and Marco Radeschi
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## Abstract:

We consider convex contact spheres $Y$ all of whose Reeb orbits are closed. Any such $Y$ admits a stratification by the periods of closed Reeb orbits. We show that $Y$ “resembles” a contact ellipsoid: any stratum of $Y$ is an integral homology sphere, and the sequence of Ekeland-Hofer spectral invariants of $Y$ coincides with the full sequence of action values, each one repeated according to its multiplicity.## References

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## Additional Information

**Marco Mazzucchelli**- Affiliation: CNRS, UMPA, École Normale Supérieure de Lyon, 69364 Lyon, France
- MR Author ID: 832298
- ORCID: 0000-0003-3782-6079
- Email: marco.mazzucchelli@ens-lyon.fr
**Marco Radeschi**- Affiliation: Department of Mathematics, University of Notre Dame, Indiana 46556
- MR Author ID: 1079099
- ORCID: 0000-0001-6167-7136
- Email: mradesch@nd.edu
- Received by editor(s): September 18, 2021
- Received by editor(s) in revised form: September 13, 2022
- Published electronically: December 15, 2022
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**376**(2023), 2125-2153 - MSC (2020): Primary 53D10, 58E05
- DOI: https://doi.org/10.1090/tran/8836
- MathSciNet review: 4549701