On chaos with additional zero Lyapunov exponents and related effects. Overview and illustrations.

Abstract

The problem of high-dimensional chaos with additional zero Lyapunov exponents is discussed. A review of both early and modern publications is presented. Specific examples of systems of different nature and model systems are considered. The review is supplemented with illustrations on the example of a discrete version of the Lorenz-84 system and a flow system consisting of subsystems with multi-frequency quasiperiodicity and chaos. Related effects such as quasi-periodic resonant tongues, quasi-periodic windows in chaos, and quasi-periodic shrimps are also discussed.