Adam Harris

University of New England (Australia)

Embedding J-holomorphic cylinders asymptotic to a Reeb orbit of elliptic type

Pseudo-holomorphic mappings of a cylinder into the symplectisation of a contact manifold M give rise to interesting questions about asymptotic behaviour near periodic orbits of the Reeb flow. In particular, when the orbit is elliptic (i.e., the linearisation of the return map along the orbit has unimodular complex eigenvalues) we examine the extent to which the map may be represented holomorphically in a tubular neighbourhood.