Floris Takens
Encyclopedia
Floris Takens 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' theorem
, which shows how to reconstruct a dynamical system from an observed time-series.
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 Lyusternik–Schnirelmann category.
After his graduate work, Takens spent a year at the IHES, 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, Netherlands
from 1972 until he retired from teaching in 1999.
Floris Takens was member of:
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
mathematician
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
known for contributions to the theory of chaotic dynamical systems
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
.
Together with David Ruelle
David Ruelle
David Pierre Ruelle is a Belgian-French mathematical physicist. He has worked on statistical physics and dynamical systems. With Floris Takens he coined the term strange attractor, and founded a new theory of turbulence...
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
Landau-Hopf theory of turbulence
In physics, the Landau-Hopf theory of turbulence, named for Lev Landau and Eberhard Hopf, was until the mid 1970s the accepted theory of how a fluid flow becomes turbulent. The theory says that as a fluid flows faster, it develops more and more Fourier modes...
. The prediction was later confirmed by experiment. Takens also established the result now known as the Takens' theorem
Takens' theorem
In mathematics, 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 a dynamical system...
, which shows how to reconstruct a dynamical system from an observed time-series.
Takens was born in Zaandam
Zaanstad
Zaanstad is a municipality in the Netherlands, in the province of North Holland. Its main town is Zaandam. It is part of the metropolitan area of Amsterdam.-Population centres:...
in the Netherlands
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
. He attended schools in The Hague
The Hague
The Hague is the capital city of the province of South Holland in the Netherlands. With a population of 500,000 inhabitants , it is the third largest city of the Netherlands, after Amsterdam and Rotterdam...
and in Zaandam before serving in the Dutch army for one year (1960–1961). At the University of Amsterdam
Universiteit van Amsterdam
The University of Amsterdam or the UvA is a public research university located in Amsterdam, the Netherlands. Founded in 1632 as the Athenaeum Illustre by the scholars Gerardus Vossius and Caspar Barlaeus, it is the third-oldest university in the Netherlands...
he concluded his undergraduate and graduate studies. He was granted a doctorate in mathematics in 1969 under the supervision of Nicolaas Kuiper
Nicolaas Kuiper
Nicolaas Hendrik "Nico" Kuiper was a Dutch mathematician, known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem.Kuiper completed his Ph.D...
for a thesis entitled The minimal number of critical points of a function on a compact manifold and the Lyusternik–Schnirelmann category.
After his graduate work, Takens spent a year at the IHES, in Bures-sur-Yvette, near Paris, where he worked with David Ruelle
David Ruelle
David Pierre Ruelle is a Belgian-French mathematical physicist. He has worked on statistical physics and dynamical systems. With Floris Takens he coined the term strange attractor, and founded a new theory of turbulence...
, René Thom
René Thom
René Frédéric Thom was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as...
, and Jacob Palis
Jacob Palis
Jacob Palis, Jr. is a Brazilian mathematician and professor. Since 1973 he has held a permanent position as professor at Instituto Nacional de Matemática Pura e Aplicada in Rio de Janeiro, Brazil. He was director of the same institute from 1993 until 2003...
. His friendship with Palis has taken him many times to the Instituto de Matemática Pura e Aplicada, IMPA, in Rio de Janeiro
Rio de Janeiro
Rio de Janeiro , commonly referred to simply as Rio, is the capital city of the State of Rio de Janeiro, the second largest city of Brazil, and the third largest metropolitan area and agglomeration in South America, boasting approximately 6.3 million people within the city proper, making it the 6th...
, Brazil
Brazil
Brazil , officially the Federative Republic of Brazil , is the largest country in South America. It is the world's fifth largest country, both by geographical area and by population with over 192 million people...
. Their collaboration produced several joint publications.
Takens was a professor at the University of Groningen
University of Groningen
The University of Groningen , located in the city of Groningen, was founded in 1614. It is one of the oldest universities in the Netherlands as well as one of its largest. Since its inception more than 100,000 students have graduated...
, in Groningen, Netherlands
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
from 1972 until he retired from teaching in 1999.
Floris Takens was member of:
- The Royal Dutch Academy of Arts and Sciences,
- The Brazilian Academy of Sciences (since 1981), and
- The editorial board for the Springer-Verlag's Lecture Notes in Mathematics.