Some elements for a history of the dynamical systems theory

Abstract

Writing a history of a scientific theory is always difficult because it requires to focus on some key contributors and to “reconstruct” some supposed influences. In the 1970s, a new way of performing science under the name “chaos” emerged, combining the mathematics from the nonlinear dynamical systems theory and numerical simulations. To provide a direct testimony of how contributors can be influenced by other scientists or works, we here collected some writings about the early times of a few contributors to chaos theory. The purpose is to exhibit the diversity in the paths and to bring some elements—which were never published—illustrating the atmosphere of this period. Some peculiarities of chaos theory are also discussed. Chaos is a word that is, in science, very often quickly associated with the overgeneralized butterfly effect, inherited from the title of a talk given in 1972 by Edward Lorenz, one of the great contributors to the so-called chaos theory. This theory is a branch of the nonlinear dynamical systems (NDS) theory, which was boosted by Poincarétextquoterights works at the late 19th century. It was then further developed by many great mathematicians for a few decades. In the 1960s, with the occurrence of computers, chaos theory emerged as a new methodology that is neither “pure” mathematics nor disconnected from the strongly mathematical NDS theory. The scientists working on chaos constitute a very interdisciplinary community whose emergence is associated with a high rate of disciplinary migration. Some of its contributors describe here how this migration occurred.

Publication
Chaos 31: 053110