Middle thirds elimination

Indeed, the logistic map for r > 4 also leads to a middle thirds elimination process, although now the middle thirds axe not exactly thirds any more. In fact, the length of the interval that leaves A after the first application of /s is 1/ 0.45. But topologically there is no difference compared with the Cantor elimination process. Therefore, in analogy to the tent map, we expect to see exponential decay of A induced by /5. This is indeed the case. An analytical approximation to the decay constant is obtained if we assume that the fraction of points that leave A in every step is the same as the firaction that leaves after the first application of fs. With this assumption we obtain Psin) = exp(—771), where 7 = ln[- /5/(- /5 — 1)]. 

An alcohol can be viewed as the product of the first step in the oxidation of a hydrocarbon, in the sense that the overall result can be considered to be the insertion of one O atom between C and H. If another O atom is inserted on the same C, and H2O eliminated, the result is an aldehyde (if the C was at the end of chain) or a ketone (if in the middle). The third step, inserting the last possible O atom on the C of an aldehyde, results in an acid. 

In fact, Heinrich suggested that accident prevention should aim to remove or eliminate the middle or third domino, representing the unsafe act, mechanical or physical hazard, thus preventing the accident. 

---