On the tree models of mildly dissipative maps

TL;DR

This paper investigates the effectiveness of tree models in representing mildly dissipative diffeomorphisms on the disk, focusing on their role as dynamical invariants in topology and ergodic theory.

Contribution

It provides an analysis of the quality of tree models as invariants for these dynamical systems, highlighting their properties and limitations.

Findings

Tree models capture ergodic aperiodic data of the systems.

Tree models serve as effective topological invariants.

The study assesses the models' fidelity to original dynamics.

Abstract

This study examines the tree models of mildly dissipative diffeomorphisms on the disk $\D$. 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.