# David Ruelle

David Ruelle ( born August 20, 1935 in Ghent, Belgium ) is a Belgian- French physicist and mathematician whose main area of work is the mathematical physics, with important works concerning statistical mechanics, quantum field theory and chaos theory.

## Life

Ruelle studied at the University of Mons Civil Engineering (Diploma 1955) and besides physics and mathematics, which he continued at the Université Libre de Bruxelles. In 1957 he received his diploma in physics in 1959 he received his PhD Res Jost at ETH Zurich on axiomatic quantum field theory. After military service 1959-1960 he was assistant and lecturer in Zurich. 1962-1964 and 1970-1971 he was a member of the Institute for Advanced Study in Princeton. 1964 until his retirement in 2000 he was a professor at the Institut des Hautes Études Scientifiques ( IHES ) in Bures -sur -Yvette, near Paris, where he has an honorary professorship today. Since then he was, inter alia, Visiting professor at Rutgers University.

Ruelle has been married since 1960 and has three children. He is a French citizen since 1984.

## Work

Ruelle made fundamental contributions to the mathematical study of statistical mechanics, the theory of dynamical systems and chaos theory. His investigation of strange attractor phenomena of dynamical systems are known ( the term led Ruelle Floris Takens with a ) and related to the Ruelle - Takens scenario of turbulence formation. Before that, you usually went with Lev Landau ( 1944) ( or turbulence in fluids ) through the excitation of a growing number of independent modes ( " eddies " ) from a path into chaos. After Ruelle / Takens, there was the possibility of a completely different, abrupt transition in a few steps. The phase space is contracted to the low-dimensional fractal structure of a " Strange Attractors ". Qualitatively, this sudden transition from Harry Swinney and Jerry Gollub (Physical Review Letters, Volume 35, 1975, p 927 ) confirmed by the example of Taylor - Couette flow between two counter-rotating cylinders. Later, other possible routes to chaos ( period doubling as according to May, James Yorke, among other things, intermittency ) were found. Which approach is taken in the turbulence of fluids, is still unknown.

## Rates and Memberships

Ruelle is since 1985 member of the French ( Academie des Sciences ) and since 2002 the U.S. National Academy of Sciences ( National Academy of Sciences). Since 2003 he is member of the Accademia Nazionale dei Lincei, he is a member of the Academia Europaea, a Fellow of the American Mathematical Society and he is an honorary member of the American Academy of Arts and Sciences.

He was Knight of the Legion of Honour in 1989. In 1983 he gave a plenary lecture at the International Congress of Mathematicians (ICM ) in Warsaw ( Turbulent Dynamical Systems ) and 1970 he was Invited Speaker on the ICM in Nice ( Etats d' equilibre of systemes infinis en mecanique statistique ).

## Works

- And randomness. Springer ( first French 1991)
- Statistical mechanics - rigorous results. New York, Benjamin 1969
- Thermodynamic formalism. Addison-Wesley 1978
- Dynamic Zeta Functions and piecewise monotone maps of the interval. American Mathematical Society, 1994
- Turbulence, strange attractors and chaos. World Scientific 1995 ( reprints )
- Chaotic evolution and strange attractors. Cambridge 1989
- Elements of differentiable dynamics and bifurcation theory. Academic Press 1989
- With F. Takens: On the nature of turbulence. In: Communications in Mathematical Physics. Volume 20, 1971, p 167-192, errata Volume 23, 1971, p 343
- Strange attractors. Mathematical Intelligencer 1980
- With J.-P. Eckmann: Ergodic theory of chaos and strange attractors. In: Reviews of Modern Physics. Volume 57, 1985, p 617
- On the asymptotic condition in Quantum Field Theory. In: Helvetica Physica Acta. Volume 35, 1962, pp. 147-163 ( Haag- Ruelle theory )
- Turbulence, Strange Attractors and Chaos ( reprints of his articles ), World Scientific, Singapore, 1995
- As mathematicians tick. Springer, 2010 ( first engl. The Mathematician 's Brain. Princeton University Press 2007)