Heteroclinical repellers imply chaos

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Original languageEnglish
Pages (from-to)1471-1489
Journal / PublicationInternational Journal of Bifurcation and Chaos
Issue number5
Publication statusPublished - May 2006


In this paper, we prove that chaos in the sense of Li-Yorke and of Devaney is prevalent in discrete systems admitting the so-called heteroclinical repellers, which are similar to the transversely heteroclinical orbits in both continuous and discrete systems and are corresponding to the snapback repeller proposed by Marotto for proving the existence of chaos in higher-dimensional systems. In addition, the concept of heteroclinical repellers is generalized to be applicable to the case with degenerate transformations. In the end, some illustrative examples are provided to illustrate the theoretical results. © World Scientific Publishing Company.

Research Area(s)

  • Heteroclinical repellers, Symbolic dynamics, Topological entropy