Zac Sloane
Chaos and the Logistic Map
February 2001
Full report (MS Word)
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Zac Sloane Chaos and the Logistic Map February 2001 |
Full report (MS Word) |
The numbers d = lim(Dan)/(Dan+1) and e = lim(en)/(en+1) above have been calculated to be approximately 4.67 and 2.50, respectively, for the logistics map. Actually, these numbers hold universally for functions which are unimodal and have quadratic maximum points. Lanford gave the first rigorous proofs, using the one-dimensional, quadratic maximum case. Computer assisted proofs have also been given by Campanino, Epstein, Ruelle, Wittwer, Koch and Schenkel.