# 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} }

. 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…

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