Complex Dynamical System for Toda Lattice

Abstract

Extending an independent variable into complex and introducing an auxiliary function, we investigate nonlinear interactions between solitons for the Toda lattice by observing behavior of zeros of the function. The Newton’s method calculating them is identified with a complex dynamical system. We present numerical results of the Fatou set on the dynamics. According to motion of solitons, the set changes surprisingly. Since soliton solutions include the exponential function, the Fatou set is different from that of the polynomial and the rational functions.