Some elements for a history of the dynamical systems theory

Christophe Letellier* (Corresponding Author), Ralph Abraham, Dima L. Shepelyansky, Otto E. Rössler, Philip Holmes, René Lozi, Leon Glass, Arkady Pikovsky, Lars F. Olsen, Ichiro Tsuda, Celso Grebogi, Ulrich Parlitz, Robert Gilmore, Louis M. Pecora, Thomas L. Carroll

*Corresponding author for this work

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Chaos is a word which 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 Poincaré’s works at the late 19th century. It was then further developed by many great mathematicians for few decades. In the 1960s, with the occurence of computers, chaos theory emerged as a new methodology which 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 occured.
Original languageEnglish
Article number053110
Number of pages21
Issue number5
Early online date7 May 2021
Publication statusPublished - 7 May 2021

Bibliographical note

Leon Glass would like to thank the Natural Sciences and Engineering Research Council (Canada) for its continuous support of curiosity-driven research for over 40 years starting with the events recounted here. He also thanks his colleagues and collaborators including Stuart Kauffman, Rafael Perez, Ronald Shymko, Michael Mackey for their wonderful insights and collaborations during the times recounted here. R.G. is endebted to the following friends and colleagues, listed in the order encountered on the road described: F. T. Arecchi, L. M. Narducci, J. R. Tredicce, H. G. Solari, E. Eschenazi, G. B. Mindlin, J. L. Birman, J. S. Birman, P. Glorieux, M. Lefranc, C. Letellier, V. Messager, O. E. Rössler, R.
Williams. U.P. would like to thank the following friends and colleagues who accompanied his first steps into the world of nonlinear phenomena: U. Dressler, I. Eick, V. Englisch, K. Geist, J. Holzfuss, T. Klinker, W. Knop, A. Kramer, T. Kurz, W. Lauterborn, W. Meyer-Ilse, C. Scheffczyk, E. Suchla and M. Wisenfeldt. The work by L. Pecora and T. Carroll was supported directly by the Office of Naval Research (ONR) and by ONR through the Naval Research Laboratory’s Basic Research Program. C.L. would like to thank Jürgen Kurths for his support to this project.


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