Studies on spaces of initial conditions for non-autonomous mappings of the plane

We study non-autonomous mappings of the plane by means of spaces of initial conditions. First, we introduce the notion of a space of initial conditions for non-autonomous systems and we study the basic properties of general equations that have spaces of initial conditions. Then, we consider the minimization of spaces of initial conditions for non-autonomous systems and we show that if a non-autonomous mapping of the plane with a space of initial conditions, and unbounded degree growth, has zero algebraic entropy, then it must be one of the discrete Painlevé equations in the Sakai classification.