A Map for Eccentric Orbits in Triaxial Potentials

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 nearly axisymmetric logarithmic potentials. The map can also be applied to triaxial, lopsided, non-power-law and rotating potentials. 1. Introduction The morphology of orbits in triaxial potentials determines the structure of triaxial galaxies. The simplest triaxial potentials are those of Stackel form, which support four major families of regular orbits (boxes, short-axis tubes, and inner and outer long-axis tubes) and no stochastic orbits (Lynden-Bell 1962, de Zeeuw 19..