The stochastic web on a spherical surface generated by simple, 3-dimensional rotational transformations

摘要

It is shown that the stochastic web (or chaotic web) on the surface of a sphere can be generated by a simple, 3-dimentional rotational map, constructed by three rotational angles about each coordinate axis: x-axis, y-axis and z-axis. It is remarkable that the rotational angles in our model do not need to be complicated functions of the coordinates. As a matter of fact, the stochastic web is found when our map only consists of one simple functional rotational angle and two constant rotational angles, under certain resonance conditions. The trajectories are computed and the 3-dimentional plots of the stochastic web on the spherical surface are also presented.