George Osipenko
Laboratory of Nonlinear Analysis,
St. Petersburg State Polytechnic University
The Ikeda map occurs in the
modeling of optical recording media (crystals). Under certain parameter values
the Ikeda map exhibits highly complicated dynamical behavior. In particular,
the Ikeda map can have infinitely many hyperbolic periodic orbits, which are
located in a bounded part of the plane, and a strange attractor (the Ikeda
attractor). The aim of the paper is to give an analysis of the topological
structure of orbits by symbolic dynamics methods (the package ASIDS) and by
methods of curves iteration (the package Line). Some possible
modifications of the Ikeda mapping are considered.
An analysis
of orbit behavior near fixed and periodic points and of bifurcations to chaos
is presented.