Exponential decay of $J$-holomorphic maps with finite energy

We prove that every finite energy $J$-holomorphic map $u(s,t):\mathbb R\times S^1 \rightarrow {\mathbb R} \times \widetilde{M}$ exponentially converges to a periodic orbit of Reeb vector field of $\tilde{M},$ as $s\to \mathrm{\infty }\mathrm{.}$