Discrete chaos induced by heteroclinic cycles connecting repellers in Banach spaces

This paper is concerned with chaos induced by heteroclinic cycles connecting repellers for maps in Banach spaces. Several criteria of chaos are established in general Banach spaces and finite-dimensional spaces, respectively, by employing the coupled-expansion theory. All the maps presented in this paper are proved to be chaotic in the sense of both Li–Yorke and Devaney or in the sense of both Li–Yorke and Wiggins or in the sense of Li–Yorke. An illustrative example is provided with computer simulations.