• Corpus ID: 254069909

Symmetric periodic Reeb orbits on the sphere

@inproceedings{Abreu2022SymmetricPR,
  title={Symmetric periodic Reeb orbits on the sphere},
  author={Miguel Abreu and Hui Li Liu and Leonardo Macarini},
  year={2022}
}

• M. Abreu, H. Liu, Leonardo Macarini
• Published 29 November 2022
• Mathematics, Physics

. A long standing conjecture in Hamiltonian Dynamics states that every contact form on the standard contact sphere S 2 n ` 1 has at least n ` 1 simple periodic Reeb orbits. In this work, we consider a refinement of this problem when the contact form has a suitable symmetry and we ask if there are at least n ` 1 simple symmetric periodic orbits. We show that there is at least one symmetric periodic orbit for any contact form and at least two symmetric closed orbits whenever the contact form is dynamically convex