Title :
Computer Assisted Rigorous Proof of Chaos in the Ikeda Map
Author :
Wang, Kaihua ; Lin, Congping ; Fu, Xinchu
Author_Institution :
Sch. of Math. & Stat., Hainan Normal Univ., Haikou, China
Abstract :
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.
Keywords :
chaos; Conley index; Ikeda map; chaos; computer assisted rigorous proof; homotopy invariant property; isolated invariant set; Arrays; Chaos; Computers; Educational institutions; Electronic mail; Indexes; Orbits; Chaos; Computer assisted proof; Conley index;
Conference_Titel :
Chaos-Fractals Theories and Applications (IWCFTA), 2011 Fourth International Workshop on
Conference_Location :
Hangzhou
Print_ISBN :
978-1-4577-1798-7
DOI :
10.1109/IWCFTA.2011.32