Chaos induced by heteroclinic cycles connecting repellers and saddles in locally compact metric spaces
From the abstract: This paper is concerned with chaos induced by heteroclinic cycles, connecting repellers and saddles for maps in locally compact metric spaces [cf. \textit{Z. Li, Y. Shi} and \textit{C. Zhang}, Chaos Solitons Fractals 36, No. 3, 746--761 (2008; Zbl 1142.37014)]. In this paper, one criterion of chaos for such types of maps, is established in locally compact metric spaces, by employing the coupled-expansion theory, where the map is only continuous in some domains of interest. In particular, one criterion of chaos in the Euclidean space \(\mathbb R^n\) is also established. The maps in the criteria are proved to have a positive topological entropy and to be chaotic in the sense of Li-Yorke. An illustrative example is provided with computer simulations.
heteroclinic cycles connecting repellers and saddles
scientific article; zbMATH DE number 5569429
scientific article