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

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

known for contributions to the theory of chaotic dynamical systems. Together with

David Ruelle David Pierre Ruelle (; born 20 August 1935) is a Belgian and naturalized French mathematical physicist. He has worked on statistical physics and dynamical systems. With Floris Takens, Ruelle coined the term ''strange attractor'', and devel ...

, he predicted that

fluid turbulence In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by Chaos theory, chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disrupt ...

could develop through a

strange attractor In the mathematics, mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor va ...

, a term they coined, as opposed to the then-prevailing theory of accretion of modes. The prediction was later confirmed by

experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs whe ...

. Takens also established the result now known as the

Takens's theorem In the study of dynamical systems, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence of observations of the state of that system. The reconstruction preserves the properti ...

, which shows how to reconstruct a dynamical system from an observed

time-series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. E ...

. He was the first to show how chaotic attractors could be learned by neural networks. Takens was born in

Zaandam Zaandam () is a city in the Provinces of the Netherlands, province of North Holland, Netherlands. It is the main city of the municipality of Zaanstad and received City rights in the Netherlands, city rights in 1811. It is located on the river Zaan ...

in the

Netherlands , Terminology of the Low Countries, informally Holland, is a country in Northwestern Europe, with Caribbean Netherlands, overseas territories in the Caribbean. It is the largest of the four constituent countries of the Kingdom of the Nether ...

. He attended schools in

The Hague The Hague ( ) is the capital city of the South Holland province of the Netherlands. With a population of over half a million, it is the third-largest city in the Netherlands. Situated on the west coast facing the North Sea, The Hague is the c ...

and in Zaandam before serving in the Dutch army for one year (1960–1961). At the

University of Amsterdam The University of Amsterdam (abbreviated as UvA, ) is a public university, public research university located in Amsterdam, Netherlands. Established in 1632 by municipal authorities, it is the fourth-oldest academic institution in the Netherlan ...

, he concluded his undergraduate and graduate studies. He was granted a doctorate in mathematics in 1969 under the supervision of

Nicolaas Kuiper Nicolaas Hendrik Kuiper (; 28 June 1920 – 12 December 1994) was a Dutch mathematician, known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem. Kuiper studied at University of Leiden in 1937- ...

for a thesis entitled ''The minimal number of critical points of a function on a compact manifold and the

Lusternik–Schnirelmann category In mathematics, the Lyusternik–Schnirelmann category (or, Lusternik–Schnirelmann category, LS-category) of a topological space X is the homotopy invariant defined to be the smallest integer number k such that there is an open covering \_ of X ...

''. After his graduate work, Takens spent a year at the

Institut des Hautes Études Scientifiques The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics (also with a small theoretical biology g ...

, in

Bures-sur-Yvette Bures-sur-Yvette (, "Bures-on- Yvette") is a commune in the Essonne department in the Île-de-France region in Northern France. It is a southern Parisian outer suburb in the Vallée de Chevreuse, with a population of 9,254 as of 2021. Geograp ...

, near Paris, where he worked with

René Thom René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French mathematician, who received the Fields Medal in 1958. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became ...

, and

Jacob Palis Jacob Palis Jr. (15 March 1940 – 7 May 2025) was a Brazilian mathematician and professor. Palis's research interests were mainly dynamical systems and differential equations. Some themes are global stability and hyperbolicity, bifurcations, ...

. His friendship with Palis took him many times to the Instituto de Matemática Pura e Aplicada (IMPA) in

Rio de Janeiro Rio de Janeiro, or simply Rio, is the capital of the Rio de Janeiro (state), state of Rio de Janeiro. It is the List of cities in Brazil by population, second-most-populous city in Brazil (after São Paulo) and the Largest cities in the America ...

, Brazil. Their collaboration produced several joint publications. Takens was a professor at the

University of Groningen The University of Groningen (abbreviated as UG; , abbreviated as RUG) is a Public university#Continental Europe, public research university of more than 30,000 students in the city of Groningen (city), Groningen, Netherlands. Founded in 1614, th ...

, in

Groningen Groningen ( , ; ; or ) is the capital city and main municipality of Groningen (province), Groningen province in the Netherlands. Dubbed the "capital of the north", Groningen is the largest place as well as the economic and cultural centre of ...

, the Netherlands from 1972 until he retired from teaching in 1999. Takens was a member of: * The

Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences (, KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed in the Trippenhuis in Amsterdam. In addition to various advisory a ...

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

Selected publications

* * * *

Notes

References

*
Floris Takens - Academia Brasileira de Ciências
Accessed on 26 January 2010.

External links

* {{DEFAULTSORT:Takens, Floris 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

Selected publications

See also

Notes

References

External links