Symbolic Dynamics in the Free-Fall Equal-Mass Three-Body Problem

Abstract

Free-fall equal-mass three-body systems are numerically studied using symbolic dynamics. We scan the two-dimensional homology map of initial configurations in steps of 0.001 along both axes. States of binary and triple encounters as well as changes of configuration are used to construct symbolic sequences. Symbolic sequences are characterized by Shannon and Markov entropies. Different ergodic components corresponding to different distinct peaks on the histograms of these entropies are revealed.