Writing the history of dynamical systems and chaos: Longue durée and revolution, disciplines and cultures

Historia Mathematica

Volumn 29, Issue 3, 2002, Pages 273-339

  Aubin, David ^a   Dalmedico, Amy Dahan ^b  

^a MAX PLANCK INSTITUTE FOR THE HISTORY OF SCIENCE   (Germany)

^b CNRS   (France)

Author keywords

Computers; Deterministic chaos; Dynamical systems; Fluid mechanics; History; Meteorology; Smale

Indexed keywords

EID: 0036686818     PISSN: 03150860     EISSN: None     Source Type: Journal    
DOI: 10.1006/hmat.2002.2351     Document Type: Article

References (322)

1. In pursuit of Birkhoff's chaotic attractor
2. Chaos, Gaia, Eros: A chaos pioneer uncovers the three great streams of history
3. Foundations of mechanics: A mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the three-body problem
4. Low-temperature studies of the Rayleigh-Bénard instability and turbulence
5. Over two decades of pattern formation, a personal perspective
6. Kolmogorov in perspective
7. Poincaré's discovery of homoclinic points
8. More is different
9. Les cycles limites de Poincaré et la théorie des oscillations auto-entretenues
10. Theory of oscillations
11. Systèmes grossiers
12. Roughness of geodesic flows on compact Riemannian manifolds of negative curvature
13. Developments in statistical reasoning and their links with mathematics
14. A renormalization group with periodic behavior
15. On A. N. Kolmogorov
16. Catastrophe theory
17. Problèmes ergodiques de la mécanique classique
18. John von Neumann and the origins of modern computing
19. Entre le cristal et la fumée. Essai sur l'organisation du vivant
20. The withering immortality of Nicolas Bourbaki: A cultural connector at the confluence of mathematics, structuralism, and the Oulipo in France
21. A cultural history of catastrophes and chaos: Around the Institut des Hautes Études Scientifiques
22. Un pacte singulier entre mathématique et industrie. L'enfance chaotique de l'Institut des hautes études scientifiques
23. Chaos et déterminisme. s.v. Dictionnaire d'histoire et de philosophie des sciences
24. Théorie du chaos: L'ordinateur en prime
25. From catastrophe to chaos: The modeling practices of "Applied topologists"
26. Forthcoming. Forms of explanations in the catastrophe theory of René Thom: Topology, morphogenesis, and structuralism
27. Oscar II's prize competition and the error in Poincaré's memoir on the three body problem
28. Poincaré and the three-body problem
29. Stephen Smale: The mathematician who broke the dimension barrier
30. The mathematician and the engineer: Statistical theories of turbulence in the 20's
31. On the history of the statistical theories of turbulence
32. Sur les courbes définies par des équations différentielles
33. History of control engineering 1930-1955
34. Time dependent velocity in Rayleigh-Bénard convection: A transition to turbulence
35. Intermittency in Rayleigh-Bénard convection
36. L'Ordre dans le chaos
37. Des rythmes au chaos
38. Turbulence seminar: Berkeley 1976/77
39. Proof of Poincaré's geometric theorem
40. Dynamical systems
41. Proof of the ergodic theorem
42. Sur quelques courbes fermées remarquables
43. Asymptotic methods in the theory of nonlinear oscillations
44. Light-scattering from nonequilibrium fluid systems
45. The higher calculus: A history of real and complex analysis from Euler to Weierstrass
46. Poincaré, philosophe et mathématicien. "Les Génies de la science"
47. Changing images in mathematics: From the French Revolution to the new millennium
48. Catastrophe theory and its critics
49. L'Invention des formes. Chaos, catastrophes, fractales, structures dissipatives, attracteurs étranges
50. La mesure de l'etat. Administrateurs et géomètres au XVIIIème siecle
51. The laser in America: 1950-1970
52. Renormalization: From Lorentz to Landau (and beyond)
53. Critical point phenomena, universal physics at large length scales
54. The conceptual foundations and the philosophical aspects of renormalization theory
55. Non-linear vibrations: A chapter in mathematical history
56. Some points in the history of the theory of nonlinear oscillations
57. 2)y′ + y = bλk cos(γt + a), k large
58. Un demi-siècle de fractales: 1870-1920
59. Les idées nouvelles de Poincaré
60. Integration of the primitive and balance equations
61. Numerical experiment in atmospheric hydrodynamics
62. Theory of ordinary differential equations
63. Iterated maps of the interval as dynamical systems
64. Universal properties of maps on the interval
65. n
66. Changing order: Replication and induction in scientific practice
67. Itérations d'endormorphismes et groupe de renormalisation
68. Critical transition to stochasticity for some dynamical systems
69. La theorie du hasard est-elle née par hasard?
70. Jurassic Park
71. Chaos
72. Le déterminisme de Pierre-Simon Laplace et le déterminisme aujourd'hui
73. La renaissance des systèmes dynamiques aux États-Unis après la deuxième guerre mondiale: L'action de Solomon Lefschetz
74. L'essor des mathématiques appliquées aux Etats-Unis: L'impact de la seconde guerre mondiale
75. La théorie des oscillations d'Andronov. Talk delivered at the conference
76. Le difficile héritage de Henri Poincaré en systèmes dynamiques
77. Pur versus applique? Un point de vue d'historien sur une "guerre d'images" La Gazette des Mathématiciens
78. Un monde moins stable qu'il n'y paraît
79. Des nuages ou des horloges
80. L'image "fin de siècle" des sciences. La théorie du chaos a-t-elle engendré une révolution scientifique?
81. History and epistemology of models: Meteorology as a case study (1946-1963)
82. An image conflict in mathematics after 1945. In changing images in mathematics: From the French Revolution to the new millennium
83. Forthcoming a. Chaos, disorder and mixing: The new "fin de siècle" image of science
84. Forthcoming b. Andronov's school and the chaos reconfiguration
85. Chaos et déterminisme
86. Andronov and the Gorki school: From auto-oscillations to radiophysics and control theory
87. Classical probability in the enlightenment
88. Dynamical systems with stable structures
89. Energy spectra of certain randomly-stirred fluids
90. Sur les courbes définies par les équations différentielles à la surface du tore
91. Itérations d'endomorphismes de la droite réelle et représentation des nombres
92. Iteration of endomorphisms on the real axis and representation of numbers
93. La politique des grands nombres. Histoire de la raison statistique. Paris: La Découverte. The politics of large numbers: A history of statistical reasoning
94. Celestial encounters: The origins of chaos and stability
95. Pour l'honneur de l'esprit humain. Les mathématiques aujourd'hui
96. Les voies du chaos déterministe dans l'école russe
97. The critical point: A historical introduction to the modern theory of critical phenomena
98. Taylor-Couette flow: The early days
99. La théorie physique. Son objet et sa structure
100. A history of electrical engineering
101. Nature's numbers by Ian Steward (review)
102. Roads to turbulence in dissipative dynamical systems
103. Le Calcul, l'imprévu. Les figures du temps de Kepler à Thom
104. Ignoring chaos
105. L'approche numérique: Simulation ou simulacre des phénomènes
106. Sur les équations fonctionnelles
107. Sur l'itération des fonctions transcendantes entières
108. Quantitative universality for a class of nonlinear transformations
109. The onset spectrum of turbulence
110. The universal metric properties of nonlinear transformations
111. Universal behavior in nonlinear systems
112. Studies of non linear problems
113. Weimar culture, causality, and quantum mechanics, 1918-1927: Adaptation by German physicists and mathematicians to a hostile intellectual environment
114. Construction de la signification physique dans le métier de physicien: Le cas du chaos déterministe, doctoral thesis
115. Image and logic: A material culture of microphysics
116. Phase transition and turbulence: An introduction
117. The new production of knowledge: The dynamics of science and research in contemporary societies
118. La théorie qualitative de Poincaré et le problème de l'intégration des équations différentielles
119. Structure, stabilité et fluctuations
120. Chaos: Making a new science
121. Fluid mechanics in the first half of this century
122. Onset of turbulence in a rotating fluid
123. Henri Poincaré: Science et philosophie
124. Poincaré, topological dynamics, and the stability of the solar system
125. The catastrophe controversy
126. The bifurcation of quadratic functions
127. Nonlinear oscillations, dynamical systems, and bifurcations of vector field
128. Sensitivity analysis and Lyapunov stability
129. Point sequences generated by two-dimensional recurrences
130. Sur les récurrences, ou transformations ponctuelles, du premier ordre, avec inverse non unique
131. Dynamique chaotique. Transformations ponctuelles, transitions ordre-désordre
132. Recurrence and discrete dynamic systems
133. Bifurcation theory and applications in scientific disciplines
134. The taming of chance
135. The social construction of what?
136. L'œuvre mathématique de Henri Poincaré
137. Henri Poincaré et le problème des trois corps
138. Chaos bound: Orderly disorder in contemporary literature and science
139. John von Neumann and Norbert Wiener from mathematics to the technologies of life and death
140. The Cybernetics Group
141. Numerical exploration of Hamiltonian systems
142. The applicability of the third integral of the motion: Some numerical experiments
143. The dynamical systems approach to differential equations
144. Poincaré, celestial mechanics, dynamical-systems theory and "chaos"
145. Abzweigung einer periodischen Lösung von eine stationären Lösung eines Differentialsystems
146. A mathematical example displaying features of turbulence
147. Bifurcation of a periodic solution from a stationary solution of a system of differential equations
148. Instability and convection in fluid layers: A report of euromech 106
149. The Ising model, computer simulation, and universal physics
150. La Mathématisation du réel
151. The IHÉS at forty
152. Logique du vivant. Une histoire de l'hérédité
153. Mémoire sur l'itération des fonctions rationnelles
154. c
155. Critical behavior: Universality and scaling
156. Scaling, universality, and operator algebra
157. From order to chaos. Essays: Critical, chaotic, and otherwise
158. Who wrote the book of life? A history of the genetic code
159. International Conference on Dynamical Systems in Mathematical Physics
160. In the wake of chaos: Unpredictable order in dynamical systems
161. The development of Galois theory from Lagrange to Artin
162. Bénard convection
163. Problèmes fondamenaux de la mécanique non linéaire
164. Introduction to non-linear mechanics: A free translation by Solomon Lefschetz of excerpts from two Russian monographs
165. Works on the foundations of statistical physics
166. Study of recurrence relationships and their applications by the Laboratoire d'automatique et de ses applications spatiales
167. On the problem of turbulence
168. A computer-assisted proof of the Feigenbaum conjectures
169. The stability and control of discrete processes
170. Sur les équations fonctionnelles qui définissent une courbe ou une surface invariante par une transformation
171. Naissance de la mortalité
172. Les systèmes auto-entretenus
173. Les systèmes autoentretenus et les oscillations de relaxation
174. Lectures on differential equations
175. Differential equations: Geometric theory
176. Nonlinear differential equations and nonlinear oscillations
177. Transformation theory of non-linear differential equations of the second order
178. A second order differential equation with singular solutions
179. Period three implies chaos
180. Une expérience de Rayleigh-Bénard de géométrie réduite: Multiplication, accrochage et démultiplication de fréquences
181. A Rayleigh-Bénard experiment: Helium in a small box
182. Étude des oscillations entretenues
183. The theory of hydrodynamic stability
184. On the origin and history of ergodic theory
185. Energy and numerical prediction
186. Maximum simplification of the dynamic equations
187. The statistical prediction of solutions of dynamic equations
188. Deterministic nonperiodic flow
189. The problem of deducing the climate from the governing equations
190. The essence of chaos
191. Problème général de la stabilité du mouvement
192. Statistics in Britain, 1865-1930: The social construction of scientific knowledge
193. Transition to turbulence in a statically stressed fluid
194. The mathematical collaboration of M. L. Cartwright and J. E. Littlewood
195. Mary Cartwright (1900-1998)
196. Some problems in the theory of nonlinear oscillations
197. Les objets fractals. Forme, hasard et dimension
198. The Hopf bifurcation and its applications
199. Instabilities, oscillations, and chaos
200. The onset of turbulence: A review of recent developments in theory and experiment
201. Colloque C1: "Hydrodynamique physique et instabilité"
202. The early reception in France of the work of Poincaré and Lyapunov in the qualitative theory of differential equations
203. Stability and complexity in model ecosystems
204. Biological populations with nonoverlapping generations, stable points, stable cycles, and chaos
205. Simple mathematical models with complicated dynamics
206. On the finite limit sets for transformations of the unit interval
207. Mathematical theories versus biological facts: A debate on mathematical population dynamics
208. Nonlinear oscillations
209. Transformation ponctuelles et leurs applications
210. Some historical aspects concerning the theory of dynamic systems
211. Some historical aspects of nonlinear dynamics, possible trends for the future
212. KAM-theory
213. Le hasard et la nécessité
214. Models as mediators: Perspectives on natural and social sciences
215. Le paradigme perdu: La nature humaine
216. La méthode. 1. La nature de la nature
217. Symbolic dynamics
218. Sur l'itération des polynômes réels quadratiques
219. Re-thinking science: Knowledge and the public in age of uncertainty
220. On the contribution of smale to dynamical systems
221. Did Poincaré really discover chaos?
222. Les grandes révolutions scientifiques du XXe siècle
223. On structural stability
224. Constructing quarks: A sociological history of particle physics
225. Mémoire sur les courbes définies par une équation différentielle
226. Sur l'équilibre d'une masse fluide animée d'un mouvement de rotation
227. Sur le problème des trois corps et les équations de la dynamique
228. Méthodes nouvelles de la mécanique céleste
229. Sur la théorie cinétique des gaz
230. Analysis situs
231. Figures d'équilibre d'une massefluide
232. Science et méthode
233. Sur un théorème de géométrie
234. Calcul des probabilités
235. Intermittency: A generic phenomenon at the onset of turbulence
236. Intermittent transition to turbulence in dissipative dynamical systems
237. La science dans la culture
238. La Querelle du déterminisme
239. The rise of statistical thinking, 1820-1920
240. Trust in numbers
241. La nouvelle alliance. Métamorphose de la science
242. Proceedings of the Conference on Instability and Disspative Structures in Hydrodynamics [Brussels, 1973]
243. Oscillating iterated sequences
244. Oscillations of a system of disk dynamos
245. Fluctuations, instabilities, and phase transitions
246. Nonlinear phenomena at phase transitions and instabilities
247. Théorie des oscillateurs
248. The Great Devonian Controversy
249. Strange attractors as a mathematical explanation of turbulence
250. Differentiable dynamical systems and the problem of turbulence
251. Hasard et chaos
252. Turbulence, strange attractors, and chaos
253. On the nature of turbulence
254. Coexistence of cycles of a continuous map of a line into itself. Ukraïnskij Matematici Zhurnal 16, 61-71
255. Deterministic chaos: An introduction
256. QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga
257. La naissance de la physique dans le texte de Lucrèce. Fleuves et turbulences
258. Hermès V. Le passage du Nord-Ouest
259. La genèse. Paris: Minuit
260. Kolmogorov: Life and creative activities
261. L'aléatoire du non-aléatoire
262. Topics in ergodic theory
263. Modeling and simulation
264. Morse inequalities for a dynamical system
265. Dynamical systems and the topological conjugacy problem for diffeomorphisms
266. Diffeomorphisms with many periodic points
267. Structurally stable systems are not dense
268. Differentiable dynamical systems
269. Personal perspectives on mathematics and mechanics
270. Review of E. C. Zeeman, Catastrophe theory [1977]
271. The mathematics of time: Essays on dynamical systems, economic processes, and related topics
272. The story of the higher dimensional Poincaré conjecture (what actually happened on the beaches of Rio)
273. Chaos: Finding a horseshoe on the beaches of Rio
274. The historiography of recent science and technology
275. Institutional ecology, "translations," and boundary objects: Amateurs and professionals in Berkeley's Museum of Vertebrate Zoology, 1907-39
276. A theorem of Šarkovskij on the existence of periodic orbits of continuous endormorphisms of the real line
277. Arcadia
278. Catastrophe theory as applied to the social and biological sciences: A critique
279. Turbulence and Navier-Stokes equations
280. Les singularités des applications différentiables
281. Sur les travaux de Stephen Smale
282. Une théorie dynamique de la morphogénèse
283. Stabilité structurelle et morphogénèse: Essai d'une théorie générale des modèles
284. La théorie des catastrophes: État présent et perspectives
285. Modèles mathématiques de la morphogénèse. Recueil de textes sur la théorie des catastrophes et ses applications
286. D'un modèle de la science à une science des modèles
287. Esquisse d'une sémiophysique. Physique aristotélicienne et théorie des catastrophes
288. Prédire n'est pas expliquer
289. A history and philosophy of fluidmechanics
290. Catastrofi: Una controversia scientifica
291. Introduction au groupe de renormalisation et à ses applications
292. The Lorenz attractor exists
293. Strange attractors and the origin of chaos
294. On relaxation-oscillations
295. Mathematics and radio problems
296. Frequency demulitiplication
297. The heart beat considered as a relaxation oscillation, and an electrical model of the heart
298. Hydrodynamic instabilities (in isotropic fluids)
299. Steady-states, limit cycles and the onset of turbulence. A few model calculations and exercises
300. What's new on Lorenz strange attractors?
301. The early history of Poincare's conjecture
302. The engineer grapples with nonlinear problems
303. Proof of the quasi-ergodic hypothesis
304. Complexity: The emerging science at the edge of chaos
305. Amplitude instability and ergodic behavior for conservative nonlinear oscillator systems
306. Le futur des mathématiques. Les grands courants de la pensée mathématique
307. Surface tension and molecular correlations near the critical point and equation of state in the neighborhood of the critical point
308. Renormalization group and critical phenomena
309. The renormalization group and critical phenomena
310. Catastrophe theory
311. Die Genesis des abstrakten Gruppen Begriffes. Berlin. The genesis of the abstract group concept: A contribution to the history of the abstract group concept
312. The concept of function up to the middle of the 19th century
313. Differential equations for the heartbeat and nerve impulse
314. Catastrophe theory: Selected papers, 1972-1977