Uniform $n$-analytic polynomial approximations of functions on rectifiable contours in $\mathbb C$

We study approximations of functions by $n$-analytic polynomials in the uniform norm on closed rectifiable Jordan curves in the complex plane. It is shown that, in contrast to the case of uniform approximations by complex polynomials, there are no topological criteria for the existence of such approximations. We obtain a criterion for the existence of $n$-analytic polynomial approximations in terms of analytic properties of these curves.