Juan F. Navarro1 and Jacques Henrard2 1 University of Alicante, Belgium 2 University of Namur, Belgium
The origin of the fractal nature of the windows through which stars may
escape from a galaxy modelized by a simple symmetric potential is
investigated. With the help of a normalized approximation of the vicinity
of an unstable periodic
orbit, we explain the spiral structures found previously by numerical
simulation by Contopoulos and coworkers. Furthermore we show that the
``simple'' spirals found are only the simplest of an infinity of
structures, constructed by embedding an infinity of spirals inside each
other. This behaviour is generic and is likely to exist in a large class of
chaotic scattering problems.