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Floris Takens (12 November 1940 – 20 June 2010)[1] mathematician known for contributions to the theory of chaotic dynamical systems .
Together with David Ruelle , he predicted that fluid turbulence could develop through a strange attractor , a term they coined, as opposed to the then-prevailing theory of accretion of modes . The prediction was later confirmed by experiment . Takens also established the result now known as the Takens's theorem , which shows how to reconstruct a dynamical system from an observed time-series . He was the first to show how chaotic attractors could be learned by neural networks.
Takens was born in Zaandam in the Netherlands . He attended schools in The Hague and in Zaandam before serving in the Dutch army for one year (1960–1961). At the University of Amsterdam , he concluded his undergraduate and graduate studies. He was granted a doctorate in mathematics in 1969 under the supervision of Nicolaas Kuiper for a thesis entitled The minimal number of critical points of a function on a compact manifold and the Lusternik–Schnirelmann category .
After his graduate work, Takens spent a year at the Institut des Hautes Études Scientifiques , in Bures-sur-Yvette , near Paris, where he worked with David Ruelle , René Thom , and Jacob Palis . His friendship with Palis has taken him many times to the Instituto de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro , Brazil. Their collaboration produced several joint publications.
Takens was a professor at the University of Groningen , in Groningen , the Netherlands from 1972 until he retired from teaching in 1999.[2]
Takens was member of:
Selected publications [ edit ]
Ruelle, David ; Takens, Floris (1971). "On the nature of turbulence". Communications in Mathematical Physics 20 3 ): 167–192. Bibcode :1971CMaPh..20..167R . doi :10.1007/BF01646553 .
Takens, Floris (1981). "Detecting strange attractors in turbulence". Lecture Notes in Mathematics . pp. 366–381.
Newhouse, Sheldon E.; Palis, Jacob Jr. ; Takens, Floris (1983). "Bifurcations and stability of families of diffeomorphisms" . Publications Mathématiques de l'IHÉS 57 doi :10.1007/BF02698773 . S2CID 102339975 .
Bakker, Rembrandt; Schouten, Jaap C.; Giles, C. Lee; Takens, Floris; Van den Bleek, Cor M. (2000). "Learning chaotic attractors by neural networks". Neural Computation . 12 10 ): 2355–2383. doi :10.1162/089976600300014971 . PMID 11032038 . S2CID 16416364 .
See also [ edit ]
^ "Floris Takens (1940–2010)" . Royal Netherlands Academy of Arts and Sciences. Retrieved 17 July 2015 .
References [ edit ]
External links [ edit ]
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a d d i t i o n a l t e r m s m a y a p p l y . B y u s i n g t h i s s i t e , y o u a g r e e t o t h e T e r m s o f U s e a n d P r i v a c y P o l i c y . W i k i p e d i a ® i s a r e g i s t e r e d t r a d e m a r k o f t h e W i k i m e d i a F o u n d a t i o n , I n c . , a n o n - p r o f i t o r g a n i z a t i o n . ● P r i v a c y p o l i c y ● A b o u t W i k i p e d i a ● D i s c l a i m e r s ● C o n t a c t W i k i p e d i a ● C o d e o f C o n d u c t ● D e v e l o p e r s ● S t a t i s t i c s ● C o o k i e s t a t e m e n t ● M o b i l e v i e w
