Iteration at the Boundary of Newton Maps

摘要

The goal of this thesis is to study degenerating families of Newton maps and to explore the relationships among compactifications of the corresponding moduli spaces. We first employ the Berkovich dynamics to investigate the weak limits of the maximal measures for Newton maps, and then give a complete description of the rescaling limits in this case. The moduli space of Newton maps admits two natural compactifications: one from geometric invariant theory, and another the from Deligne-Mumford compactification. We construct a moduli space of marked Berkovich trees of spheres and relate it to different compactifications of the moduli spaces of Newton maps.