Noncontractible periodic orbits, Gromov invariants, and
Floer-theoretic torsions -- Yi-Jen Lee, November 15, 2002

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The existence of periodic orbits is an important problem in
dynamical systems, and in symplectic topology such existence
results are typically a manifestation of the `rigidity'
phenomenon. However, to date most such results are
restricted to CONTRACTIBLE periodic orbits. We shall explain
how variants of the Floer-theoretic torsions we have defined
previously may be used to obtain some existence results for
NONcontractible period orbits (of symplectic vector fields),
via their relation with certain Gromov-type invariants.