Small divisor problem in dynamical systems and analytic solutions of a \(q\)-difference equation with a singularity at the origin (Q606395)

The authors consider the existence of locally analytic solutions of the \(q\)-difference equation \[ \sum_{j=0}^k \sum_{t=1}^\infty C_{t,j}(z)\,\big( y(q^jz) \big)^t =G(z) \] in \({\mathbb C}\), where \(z=0\) is a pole of the functions \(C_{t,j}(z)\) for \(t\in{\mathbb N}\), \(j\in\{0,1,\dots,k\}\), with order \(h_1\) and a pole of \(G(z)\) with order \(h_2\).