Quasi-geodesics and backward orbits under semigroups of holomorphic functions (2207.10110v2)

Abstract: We explore two properties of backward orbits under semigroups of holomorphic self-maps in the unit disk. First, we prove that regular backward orbits are quasi-geodesics for the hyperbolic distance of the unit disk. Then, we show that backward orbits satisfy a useful property, this time in Euclidean terms.