Study of Recurrence Relationships and their Applications by the Laboratoire D'Automatique Et De Ses Applications Spatiales

Lagasse, J.; Mira, C.

doi:10.1016/s1474-6670(17)68321-6

Cited by 2 publications

(1 citation statement)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From 1964 to 1974, Hénon and Heiles in France, McMillan, Ford, and Bartlett in the United States, as well as Gumowski at CERN, had used this tool for problems stemming from celestial mechanics or accelerator design and the study of homoclinic and heteroclinic structures. Collaborating with Gumowski especially, Mira had set up at the LAAS a whole research group, supervised the doctorates of a half-dozen students, and associated the analytic and numeric study of bifurcations for two-dimensional recurrences with numerous applications in the theory of automatic control, integral pulse frequency modulation, and ACDC rectifiers, as well as other mathematical fields such as differential equation theory (for a survey, see [Lagasse & Mira 1972]). Following Poincaré, Lyapunov, Andronov, and Malkin, they paid a special attention to questions of stability.…”

Section: Computer and Engineering Mathematicsmentioning

confidence: 99%

Writing the History of Dynamical Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures

Aubin

Dalmedico

2002

Historia Mathematica

133

View full text Add to dashboard Cite

Between the late 1960s and the beginning of the 1980s, the wide recognition that simple dynamical laws could give rise to complex behaviors was sometimes hailed as a true scientific revolution impacting several disciplines, for which a striking label was coined-"chaos." Mathematicians quickly pointed out that the purported revolution was relying on the abstract theory of dynamical systems founded in the late 19th century by Henri Poincaré who had already reached a similar conclusion. In this paper, we flesh out the historiographical tensions arising from these confrontations: longue-durée history and revolution; abstract mathematics and the use of mathematical techniques in various other domains. After reviewing the historiography of dynamical systems theory from Poincaré to the 1960s, we highlight the pioneering work of a few individuals (Steve Smale, Edward Lorenz, David Ruelle). We then go on to discuss the nature of the chaos phenomenon, which, we argue, was a conceptual reconfiguration as much as a sociodisciplinary convergence. C 2002 Elsevier Science (USA) Entre la fin des années 1960 et le début des années 1980, la reconnaissance du fait que des lois dynamiques simples peuvent donner naissanceà des comportements très compliqués aété souvent ressentie comme une vraie révolution concernant plusieurs disciplines en train de former une nouvelle science, la "science du chaos." Rapidement, les mathématiciens ont réagi en soulignant l'ancienneté de la théorie des systèmes dynamiques fondéeà la fin du XIXème siècle par Henri Poincaré qui avait déjà obtenu ce résultat précis. Dans cet article, nous mettons enévidence les tensions historiographiques issues de diverses confrontations: l'histoire de longue durée versus la notion de révolution, les mathématiques pures versus l'utilisation des techniques mathématiques dans d'autres domaines.1 A first version of this paper was delivered at the workshop "Epistémologie des Systèmes dynamiques," Paris, November 25-26, 1999. We thank the organizers and our colleagues from the sciences (and especially Yves Pomeau) for their useful comments. In the course of our research, interviews have been conducted and letters exchanged with various people; we thank in particular Vladimir Arnol'd, Alain Chenciner, Pedrag Cvitanovic, Monique Dubois, Marie Farge, Mitchell Feigenbaum, Micheal Hermann, Igor Gumowski, Edward Lorenz, Jacques Laskar, Paul Manneville, Paul C. Martin, Christian Mira, Mauricio Peixoto, David Ruelle, René Thom, and JeanChristophe Yoccoz. For their comments on parts of this paper, we thank Umberto Bottazzini, Philip J.

show abstract

Section: Computer and Engineering Mathematicsmentioning

confidence: 99%