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We construct an example of a smooth map $\mathbb{C}\to\mathbb{C}^2$ whichvanishes to infinite order at the origin, and such that the ratio of the normof the $\bar z$ derivative to the norm of the $z$ derivative also vanishes toinfinite order. This gives a counterexample to strong unique continuation for avector valued analogue of the Beltrami equation.

Smooth counterexamples to strong unique continuation for a Beltrami system in $\mathbb{C}^2$