|Oh what a tangled web we weave ...|
|SIR WALTER SCOTT|
A stochastic web is a web-like structure in the phase space of a classical dynamical system (normally with a single degree of freedom) -- in the present case: of the kicked harmonic oscillator. This structure completely covers the phase space and possesses certain (approximate) symmetry properties: rotational and, in some cases, translational invariance. The dynamics on the web can be given, for example, by ZASLAVSKY's web map. There are two distinct types of dynamics in the web: regular motion in the meshes of the web and irregular, stochastic motion in the channels; the second provides the motivation for characterizing the web as ``stochastic''.
Stochastic webs can be obtained by considering suitable discrete mappings derived from the classical dynamics of the kicked harmonic oscillator. I therefore begin the exposition of the subject in section 1.1 by introducing and briefly discussing this model system. Then, in section 1.2, I make use of the kicked harmonic oscillator to generate the stochastic webs that are in the focus of interest here and provide the classical background for the entire present study. Finally, in section 1.3, I address the complementary case characterized by nonexistence of stochastic webs.