I would like to know if following is correct.


**Statement.** Suppose we have a smooth (i.e., $C^\infty$) almost complex structure on $\mathbb R^4$ and $C\_1, C\_2$ are two $J$-holomorphic curves passing through $(0,0)$, tangent at $(0,0)$ and regular at $(0,0)$. Then there exist $C^{\infty}$ smooth complex coordinates $(z,w)$ such that $C\_1$ is locally given by $w=0$ and $C\_2$ by $w=z^n$.


PS. I think it would be enough for me to know that $C\_2$ can be given by $w=z^n+O|z^{n+1}|$. However everything must be $C^{\infty}$ - the coordinates, and the $O|z^{n+1}|$ term. If, on the other hand one can not expect to have a $C^{\infty}$ diffeo, what is the best one can expect?



Two smooth tangent almost complex curves in a $4$-manifold
This follows from theorem 6.2 (and the first sentence in the proof) of Mario J. Micallef and Brian White, *The structure of branch points in minimal surfaces and in pseudoholomorphic curves*, **Ann. of Math.** (2) 141 (1995), no. 1, 35–85.


