Chaos induced by heteroclinic cycles connecting repellers and saddles in locally compact metric spaces

Abstract

This paper is concerned with chaos induced by heteroclinic cycles, connecting repellers and saddles for maps in locally compact metric spaces. 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 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.