Fast Lyapunov Indicators OFLI and OMEGNO: Their Relationship and Special Features

Abstract

The orthogonal fast Lyapunov indicator (OFLI) and the modification of the mean exponential growth factor of nearby orbits (MEGNO) proposed recently and called the orthogonal MEGNO indicator (OMEGNO) are compared theoretically and numerically. It is shown that these indicators are expressed in terms of the same base function. Moreover, the OMEGNO, as well as the OFLI, is expressed analytically through the base function. A numerical comparison is performed on examples of studying the dynamics in the planar circular restricted three-body problem. These examples help one to understand the special features in the performance of both indicators.