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Floris Takens
Floris Takens at the University of Warwick in 1980 (photo from Mathematical Research Institute of Oberwolfach)
Born	(1940-11-12)12 November 1940 Zaandam, Netherlands
Died	20 June 2010(2010-06-20) (aged 69)
Nationality	Dutch
Alma mater	University of Amsterdam
Known for	Takens's theorem
Scientific career
Fields	Mathematics
Doctoral advisor	Nicolaas Kuiper

Floris Takens (12 November 1940 – 20 June 2010) was a Dutch 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.

Takens was member of:

• The Royal Netherlands Academy of Arts and Sciences (since 1991)
• The Brazilian Academy of Sciences (since 1981), and
• The editorial board for the Springer-Verlag's Lecture Notes in Mathematics.

Selected publications

• 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: 1–71. 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

• Bogdanov–Takens bifurcation

Notes

1. rug.nl Archived 2010-12-11 at the Wayback Machine (retrieved 30 October 2010)
2. dynamicalsystems.org (retrieved 30 October 2010)
3. "Floris Takens (1940–2010)". Royal Netherlands Academy of Arts and Sciences. Retrieved 17 July 2015.

References

• Broer, Henk W.; Krauskopf, Bernd; Vegter, Gert, eds. (2001). Global Analysis of Dynamical Systems festschrift dedicated to Floris Takens for his 60th birthday. IOP Publishing. ISBN 0-7503-0803-6.
• Floris Takens - Academia Brasileira de Ciências. Accessed on 26 January 2010.

External links

• Floris Takens at the Mathematics Genealogy Project

v t e Chaos theory
Concepts	Core Attractor Bifurcation Fractal Limit set Lyapunov exponent Orbit Periodic point Phase space Anosov diffeomorphism Arnold tongue axiom A dynamical system Bifurcation diagram Box-counting dimension Correlation dimension Conservative system Ergodicity False nearest neighbors Hausdorff dimension Invariant measure Lyapunov stability Measure-preserving dynamical system Mixing Poincaré section Recurrence plot SRB measure Stable manifold Topological conjugacy Theorems Ergodic theorem Liouville's theorem Krylov–Bogolyubov theorem Poincaré–Bendixson theorem Poincaré recurrence theorem Stable manifold theorem Takens's theorem
Theoretical branches	Bifurcation theory Control of chaos Dynamical system Ergodic theory Quantum chaos Stability theory Synchronization of chaos
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Chaos theorists	Michael Berry Rufus Bowen Mary Cartwright Chen Guanrong Leon O. Chua Mitchell Feigenbaum Peter Grassberger Celso Grebogi Martin Gutzwiller Brosl Hasslacher Michel Hénon Svetlana Jitomirskaya Bryna Kra Edward Norton Lorenz Aleksandr Lyapunov Benoît Mandelbrot Hee Oh Edward Ott Henri Poincaré Itamar Procaccia Mary Rees Otto Rössler David Ruelle Caroline Series Yakov Sinai Oleksandr Mykolayovych Sharkovsky Nina Snaith Floris Takens Audrey Terras Mary Tsingou Marcelo Viana Amie Wilkinson James A. Yorke Lai-Sang Young
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• 1940 births
• 2010 deaths
• Chaos theorists
• Dutch systems scientists
• Members of the Brazilian Academy of Sciences
• Members of the Royal Netherlands Academy of Arts and Sciences
• People from Zaanstad
• University of Groningen alumni
• Dynamical systems theorists
• 20th-century Dutch mathematicians
• 21st-century Dutch mathematicians
• University of Amsterdam alumni