  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, fully classify the behavior of semisimple isometries of
a CAT(0) space in the associated curtain model, and prove that an isometry is
contracting in a CAT(0) space if and only if it becomes loxodromic in the
curtain model. Additionally, we exclude the presence of parabolic actions 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.
