On the Tree Models of Mildly Dissipative Maps

This study examines the tree models of mildly dissipative diffeomorphisms on the disk \({{\mathbb {D}}}\) $\mathbb{D}$ . These models are one-dimensional dynamical systems with ergodic aperiodic data as well as some properties of the original dynamics. The focus of this work is their quality as dynamical invariants in both the topological and ergodic sense.