Computer Assisted Rigorous Proof of Chaos in the Ikeda Map

This paper presents a computer assisted rigorous proof of chaos in the Ikeda map based on Conley index. It is shown that the Ikeda map with particular parameters has an isolated invariant set containing two periodic points of period 2 and 3, and a heteroclinic orbit connecting them, then a semiconjugacy between the invariant set and a nontrivial subshift system is established, which implies the Ikeda map is chaotic. By the homotopy invariant property of the Conley index, all the proof are rigorous.