Rubio–Massegu's conjecture on openness of the good set

Let $f:D\to\mathbb{C}$ be a rational function, where $D$ is its natural domain, and assume that $f$ depends effectively on its last variable. Consider the associated difference equation

$$, with good set consisting of initial conditions whose forward solutions remain defined. **Rubio–Massegu's conjecture.** The good set of$$

is open if and only if the equation is globally periodic. The conjecture links openness of the good set to global periodicity for rational difference equations. The source places it among open problems and attributes it to Rubio and Massegu; no resolution is given.