Mapping for the asteroidal resonances

Abstract

A generalized approach is presented to obtaining a mapping for the main second, third and fourth-order asteroidal resonances. One computer program then works for all these resonances. The relevant coefficients in the disturbing function must be known. The mapping was determined for the planar-elliptic, restricted, three body problem. Terms up to the fourth degree in eccentricities were taken into account. The mapping calculations are used for surface of section calculations and for calculating of Lyapunov characteristic exponents. These methods are useful in studying chaotic regions connected with resonances