An overview of 0-1 test for chaos

0-1 test for chaos provides a simple method that can be used to detect the occurrence of non-regular stationary responses of dynamical systems of any sort. Besides the simplicity of its implementation, the mathematical background of the method is based on the analysis of the long-term behavior of the extension of the underlying dynamical system with respect to the two-dimensional Euclidean group, a notion that is likely to be not very familiar to most users of the method. It is perhaps for this reason that, while in the recent years the test is gaining increasing popularity, comparatively less attention has been devoted to the discussion of its motivations. The purpose of this paper is twofold: on one hand to discuss the mathematical background of the method and, on the other, to provide an overview of the main applications of 0-1 test.