Numerical investigation of the transition from conservative to weakly-dissipative dynamics

Abstract

[en] Sometimes, conservative dynamical systems model an idealization of real-life processes, but non-conservative forces, such as friction, can play an important role in the (long-term) evolution of the system, and hence they must be considered in order to describe the process more accurately. The main goal of this work is to study the transition from conservative to weakly-dissipative dynamics. To this end, we consider the effect of dissipation in area-preserving maps. The structure of the conservative phase space is explained in the first chapter with the help of several numerical illustrations. In the second chapter, we design some numerical experiments in order to investigate some of the properties of the transition to the dissipative regime, along with a general description of this scenario.