Horseshoes and Arnold Diffusion for Hamiltonian Systems on Lie Groups

Abstract not availabl

Computing planar and spherical choreographies

An algorithm is presented for numerical computation of choreographies in the plane in a Newtonian potential and on the sphere in a cotangent potential. It is based on stereographic projection, approximation by trigonometric polynomials, and quasi-Newton and Newton optimization methods with exact gradient and exact Hessian matrix. New choreographies on the sphere are presented

Elliptical Galaxy Dynamics

A review of elliptical galaxy dynamics, with a focus on nonintegrable models. Topics covered include torus construction; modelling axisymmetric galaxies; triaxiality; collisionless relaxation; and collective instabilities.Comment: 97 Latex pages, 14 Postscript figures, uses aastex. To appear in Publications of the Astronomical Society of the Pacific, February 199