Curtain Model for CAT(0) Spaces and Isometries

Abstract

This paper studies the dynamics of isometries in the curtain model, which is used to capture the hyperbolicity in a fixed CAT(0) space. We establish several fundamental properties and fully classify the behavior of semisimple isometries of a CAT(0) space in the associated curtain model. In the nonsemisimple case, we restrict the behavior of parabolic actions with positive translation length in the curtain model in most cases of interest, allowing the use of ping-pong-like techniques on the curtain model to provide insights into the study of CAT(0) groups.