Attractors/Basin of Attraction

Abstract

It is a controversial issue to decide who first coined the term “attractor”. According to Peter Tsatsanis, the editor of the English version of Prédire n’est pas expliquer, it was René Thom who first introduced such a term. It is necessary, however, to remember that Thom thought that it was first introduced by the American mathe- matician Steven Smale, “although Smale says it was Thom that coined the neolo- gism “attractor”“(Tsatsanis 2010: 63–64 n. 20). From this point of view, Bob Williams expressed a more cautious opinion by saying that “the word “attractor” was invented by these guys, Thom and Smale” (Cucker and Wong 2000: 183). But other mathematicians are of the opinion that the term “attractor” was introduced neither by René Thom nor by Steve Smale (cf. at least Milnor 1985: 177– 178). In short, the “authorship” of such a word cannot be easily established. Despite this, the etymology of “attractor” is transparent: this word comes from the Latin attrahere, a verb which literally means “to pull” or “to drawn to” (de Vries 2012: 541). Indeed, an attractor is generally a mathematical object “that represents a steady stable state adopted by a dynamic system” (Kim et al. 2013: 1): such a state “attracts the dynamics of the system” (Bernal and Gomez 2014: 61), or, in other words, it is a stable state towards which the behaviour of the system is moving over time (see dynamic system).