A map for eccentric orbits in non-axisymmetric potentials

Abstract

We construct a simple symplectic map to study the dynamics of eccentric orbits in non-spherical potentials. The map offers a dramatic improvement in speed over traditional integration methods, while accurately representing the qualitative details of the dynamics. We focus attention on planar, non-axisymmetric power-law potentials, in particular the logarithmic potential. We confirm the presence of resonant orbit families ('boxlets') in this potential and uncover new dynamics such as the emergence of a stochastic web in early axisymmetric logarithmic potentials. The map can also be applied to triaxial, lopsided, non-power-law and rotating potentials. © 1997 RAS.