The Asymptotic Behavior of a Finite Energy Plane

Given a compact 3-manifold M equipped with the contact form λ we consider smooth maps u : C → R × M solving the Cauchy-Riemann equations Tu ̊ i = J(u) ̊ Tu, for a distinguished class of almost complex structures J on R ×M which are R-invariant and related to λ. If the map is non constant and of finite energy, the projection into M necessarily approaches as |z| → ∞ a periodic solution of the Reeb vector field associated with the contact form. Assuming the periodic solution to be non degenerate we shall describe the asymptotic behavior of the map u. The paper is a revised version of [5] and includes also [6].