Fractal behavior in classical collisional energy transfer

Abstract

A plot of final vibrational action vs initial vibrational phase for a two degree of freedom model for He + I2 collisions is examined and shown to exhibit a chattering region. The chattering region is shown to exhibit a very intricate structure, including an infinite number of regions of regularity which we term icicles. Structure is evident on all scales of examination and a fractal dimension close to 2 is obtained for some parts of the chattering region. The survival probability associated with the complexes shows an initial fast decay, due to the icicles, but can be roughly characterized over a longer and wider time range by a more slowly decaying exponential.