Recursive constructions of k-normal polynomials over finite fields

The paper is devoted to produce infinite sequences of $k$-normal polynomials $F_u(x)\in {\mathbb{F}}_q[x]$ of degrees $n{p}^u(u\ge 0)$, for a suitably chosen initial $k$-normal polynomial $F_0(x)\in {\mathbb{F}}_q[x]$ of degree $n$ over ${\mathbb{F}}_q$ by iteratively applying the transformation $x\to \frac{x^p-x}{x^p-x+\delta }$, where $\delta \in {\mathbb{F}}_q$ and $0\le k\le n-1$.