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David P. Ruelle
David Ruelle (1973)
Born	(1935-08-20) 20 August 1935 (age 89) Ghent, Belgium
Nationality	Belgian French
Alma mater	Free University of Brussels
Known for	Dobrushin–Lanford–Ruelle equations Haag–Ruelle scattering theory Ruelle zeta function Sinai–Ruelle–Bowen measure
Awards	Dannie Heineman Prize for Mathematical Physics (1985) Boltzmann Medal (1986) Holweck Prize (1993) Matteucci Medal (2004) Henri Poincaré Prize (2006) Max Planck Medal (2014) Dirac Medal (2022)
Scientific career
Fields	Mathematical physics
Institutions	ETH Zurich Institute for Advanced Study Institut des Hautes Études Scientifiques Rutgers University
Doctoral students	Giovanni Gallavotti

David Pierre Ruelle (French: [david pjɛʁ ʁɥɛl]; 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 developed a new theory of turbulence.

Biography

Ruelle studied physics at the Free University of Brussels, obtaining a PhD degree in 1959 under the supervision of Res Jost. He spent two years (1960–1962) at the ETH Zurich, and another two years (1962–1964) at the Institute for Advanced Study in Princeton, New Jersey. In 1964, he became professor at the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France. Since 2000, he has been an emeritus professor at IHES and distinguished visiting professor at Rutgers University.

David Ruelle made fundamental contributions in various aspects of mathematical physics. In quantum field theory, the most important contribution is the rigorous formulation of scattering processes based on Wightman's axiomatic theory. This approach is known as the Haag–Ruelle scattering theory. Later Ruelle helped to create a rigorous theory of statistical mechanics of equilibrium, that includes the study of the thermodynamic limit, the equivalence of ensembles, and the convergence of Mayer's series. A further result is the Asano-Ruelle lemma, which allows the study of the zeros of certain polynomial functions that are recurrent in statistical mechanics.

The study of infinite systems led to the local definition of Gibbs states or to the global definition of equilibrium states. Ruelle demonstrated with Roland L. Dobrushin and Oscar E. Lanford that translationally invariant Gibbs states are precisely the equilibrium states.

Together with Floris Takens, he proposed the description of hydrodynamic turbulence based on strange attractors with chaotic properties of hyperbolic dynamics.

Honors and awards

Since 1985 David Ruelle has been a member of the French Academy of Sciences and in 1988 he was Josiah Willard Gibbs Lecturer in Atlanta, Georgia. Since 1992 he has been an international honorary member of the American Academy of Arts and Sciences and since 1993 ordinary member of the Academia Europaea. Since 2002 he has been an international member of the United States National Academy of Sciences and since 2003 a foreign member of the Accademia Nazionale dei Lincei. Since 2012 he has been a fellow of the American Mathematical Society.

In 1985 David Ruelle was awarded the Dannie Heineman Prize for Mathematical Physics and in 1986 he received the Boltzmann Medal for his outstanding contributions to statistical mechanics. In 1993 he won the Holweck Prize and in 2004 he received the Matteucci Medal. In 2006 he was awarded the Henri Poincaré Prize and in 2014 he was honored with the prestigious Max Planck Medal for his achievements in theoretical physics. In 2022, Ruelle was awarded the ICTP's Dirac Medal for Mathematical Physics, along with Elliott H. Lieb and Joel Lebowitz, "for groundbreaking and mathematically rigorous contributions to the understanding of the statistical mechanics of classical and quantum physical systems".

Selected publications

• Ruelle, David (1993). Chance and chaos. Vol. 110. Princeton University Press. ISBN 978-0691021003; pbk{{cite book}}: CS1 maint: postscript (link) ISBN 978-0691085746; hbk
• Ruelle, David (1999). Statistical mechanics: Rigorous results. World Scientific. ISBN 978-9810238629. 1st edition 1969
• Ruelle, David (2004). Thermodynamic formalism: the mathematical structure of equilibrium statistical mechanics. Cambridge University Press. ISBN 978-0521546492. 1st edition 1978
• Ruelle, David (2004). Dynamical zeta functions for piecewise monotone maps of the interval. American Mathematical Society. ISBN 978-0821836019.
• Ruelle, David (1995). Turbulence, strange attractors and chaos. World Scientific. ISBN 978-9810223113.
• Ruelle, David (2008). Chaotic evolution and strange attractors. Vol. 1. Cambridge University Press. ISBN 978-0521368308. 1989 edition
• Ruelle, David (2014). Elements of differentiable dynamics and bifurcation theory. Elsevier. ISBN 978-1483245881. 1989 1st edition
• Ruelle, David; Takens, Floris (1971). "On the nature of turbulence". Les rencontres physiciens-mathématiciens de Strasbourg. 12: 1–44.
• Ruelle, David (1995). "Turbulence, Strange Attractors, and Chaos". World Scientific. 16: 195. Bibcode:1995tsac.book.....R.
• Eckmann, Jean-Pierre; Ruelle, David (1985). "Ergodic theory of chaos and strange attractors". Reviews of Modern Physics. 57 (3): 617–656. Bibcode:1985RvMP...57..617E. doi:10.1103/RevModPhys.57.617.
• Ruelle, David (1962). "On the asymptotic condition in quantum field theory". Helvetica Physica Acta. 35: 147–163. doi:10.5169/seals-113272.
• Ruelle, David (2007). The mathematician's brain. Princeton University Press. ISBN 978-0691129822.
• Ruelle, David (2011). L'Étrange Beauté des mathématiques (in French). Odile Jacob. ISBN 978-2738126245.

See also

• Axiomatic quantum field theory
• Chaos theory
• Dynamical systems theory
• Dobrushin–Lanford–Ruelle equations
• Fluid mechanics
• Haag–Ruelle scattering theory
• Ruelle zeta-function
• Sinai–Ruelle–Bowen measure
• Statistical physics
• Strange attractor
• Transfer operator

References

1. 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. S2CID 17074317.
2. Ruelle, David. "'What is a... Strange Attractor?" (PDF). American Mathematical Society. Retrieved 12 March 2021.
3. David Ruelle at the Mathematics Genealogy Project
4. "Biography from his website". ihes.fr. Retrieved 12 March 2021.
5. Ruelle, David (1962). "On the asymptotic condition in quantum field theory". Helvetica Physica Acta. 35: 147–163. doi:10.5169/seals-113272.
6. Ruelle, David (1999). Statistical mechanics: Rigorous results. World Scientific. ISBN 978-9810238629.
7. Ruelle, David (1971). "Extension of the Lee-Yang circle theorem". Physical Review Letters. 26 (6): 303. Bibcode:1971PhRvL..26..303R. doi:10.1103/PhysRevLett.26.303.
8. Lebowitz, Joel L.; Pittel, Boris; Ruelle, David; Speer, Eugene R. (2016). "Central limit theorems, Lee--Yang zeros, and graph-counting polynomials". Journal of Combinatorial Theory. Series A. 141: 147–183. arXiv:1408.4153. doi:10.1016/j.jcta.2016.02.009. S2CID 11664411.
9. Ruelle, David (1978). "Thermodynamic formalism. Addison Wesley, Reading". Mass zbMATH.
10. Ruelle, David (1993). Chance and chaos. Vol. 110. Princeton University Press. ISBN 978-0691021003.
11. Gallavotti, Giovanni. "Laudatio on the occasion of the Henri Poincaré Prize". International Association of Mathematical Physics. Retrieved 12 March 2021.
12. "French Academy of Sciences member page of David Ruelle". French Academy of Sciences (in French). Retrieved 13 March 2021.
13. "Josiah Willard Gibbs Lectures". American Mathematical Society. Retrieved 9 March 2021.
14. "Ruelle's member page of the American Academy of Arts and Sciences". American Academy of Arts and Sciences. Retrieved 13 March 2021.
15. "Ruelle's member page of Academia Europaea". Academia Europaea. Retrieved 13 March 2021.
16. "Ruelle's member page of the National Academy od Sciences". National Academy od Sciences. Retrieved 13 March 2021.
17. "Lincei's member page of David Ruelle". Accademia Nazionale dei Lincei. Retrieved 12 March 2021.
18. "List of Fellows of the American Mathematical Society". American Mathematical Society. Retrieved 12 March 2021.
19. "1985 Dannie Heineman Prize for Mathematical Physics Recipient". American Physical Society. Retrieved 12 March 2021.
20. "C3: Awards - The Boltzmann Medal". International Union of Pure and Applied Physics. 8 March 2021. Retrieved 12 March 2021.
21. "Fernand Holweck Medal and Prize recipients". Institute of Physics. Retrieved 12 March 2021.
22. "Medaglia Matteucci". Accademia Nazionale delle Scienze detta dei XL. Retrieved 12 March 2021.
23. "Henri Poincaré Prize winners". International Association of Mathematical Physics. Retrieved 9 March 2021.
24. "Max Planck Medal Prize winners". German Physical Society (in German). Retrieved 12 March 2021.
25. "ICTP's Dirac Medal for Mathematical Physics Recipient". ICTP-date=August 8, 2022.
26. "Review of Chance and Chaos by David Ruelle". Publishers Weekly. 2 December 1991.
27. Lieb, Elliott (1970). "Book Review: Statistical Mechanics by David Ruelle". Bulletin of the American Mathematical Society. 76 (4): 683–689. doi:10.1090/S0002-9904-1970-12505-8.
28. Babbitt, D. G. (1979). "Book Review: Thermodynamic formalism: The mathematical structures of classical equilibrium statistical mechanics by David Ruelle". Bulletin of the American Mathematical Society. 1 (6): 931–936. doi:10.1090/S0273-0979-1979-14695-0.
29. Shub, Michael (1991). "Book Review: Elements of differentiable dynamics and bifurcation theory by David Ruelle". Bulletin of the American Mathematical Society. 24: 199–212. doi:10.1090/S0273-0979-1991-15989-6.
30. Boslaugh, Sarah (23 August 2007). "Review of The Mathematician's Brain by David Ruelle". MAA Reviews, Mathematical Association of America.

External links

• David Ruelle at the Mathematics Genealogy Project
• Literature by and about David Ruelle in the German National Library catalogue.
• David Ruelle at zbMATH.
• Takens, Floris. "Laudatio for David Ruelle" (PDF). math.leidenuniv.nl. Archived from the original (PDF) on 6 March 2009.
• Gallavotti, Giovanni. "Laudatio on the occasion of the Henri Poincaré Prize". International Association of Mathematical Physics. Retrieved 12 March 2021.
• Ruelle, David. "'What is a... Strange Attractor?" (PDF). American Mathematical Society. Retrieved 12 March 2021.
• "Biography from his website". ihes.fr. Retrieved 12 March 2021.
• "David Ruelle | April 7, 2022 | A Natural Limitation for Properly Human Scientific Progress". YouTube. Mathematical Picture Language. 7 April 2022.

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
Chaotic maps (list)	Discrete Arnold's cat map Baker's map Complex quadratic map Coupled map lattice Duffing map Dyadic transformation Dynamical billiards outer Exponential map Gauss map Gingerbreadman map Hénon map Horseshoe map Ikeda map Interval exchange map Irrational rotation Kaplan–Yorke map Langton's ant Logistic map Standard map Tent map Tinkerbell map Zaslavskii map Continuous Double scroll attractor Duffing equation Lorenz system Lotka–Volterra equations Mackey–Glass equations Rabinovich–Fabrikant equations Rössler attractor Three-body problem Van der Pol oscillator
Physical systems	Chua's circuit Convection Double pendulum Elastic pendulum FPUT problem Hénon–Heiles system Kicked rotator Multiscroll attractor Population dynamics Swinging Atwood's machine Tilt-A-Whirl Weather
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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• 1935 births
• Living people
• 20th-century French mathematicians
• 21st-century French mathematicians
• Belgian mathematicians
• Belgian physicists
• Chaos theorists
• Free University of Brussels (1834–1969) alumni
• Members of the French Academy of Sciences
• Foreign associates of the National Academy of Sciences
• Recipients of the Great Cross of the National Order of Scientific Merit (Brazil)
• Fellows of the American Mathematical Society
• Academic staff of ETH Zurich
• Institute for Advanced Study visiting scholars
• Rutgers University faculty
• Recipients of the Matteucci Medal
• Belgian emigrants to France
• Winners of the Max Planck Medal
• Mathematical physicists
• Statistical physicists