Speaker: Miguel Abreu (Instituto Superior Tecnico Lisboa)
Title: Symmetric periodic Reeb orbits on the sphere and
contact homology of Lens spaces
Abstract: A long standing conjecture in Hamiltonian Dynamics states that
every contact form on the standard contact sphere $S^{2n+1}$
has at least $n+1$ simple periodic Reeb orbits. In this talk
we will consider a refinement of this problem when the contact
form has a suitable symmetry and 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
there are at least two symmetric periodic orbits whenever the
contact form is dynamically convex. A relevant ingredient in
the proof of this later result is a contact homology computation
for arbitrary Lens spaces. This is joint work with Hui Liu and
Leonardo Macarini.
