Jean-Pierre Eckmann
Jean-Pierre Eckmann | |
|---|---|
 Jean-Pierre Eckmann (right) 2007 with Albrecht Dold, John Milnor, Dietmar Salamon (from left to right) | |
| Born | 27 January 1944 |
| Nationality | Swiss |
| Alma mater | University of Geneva |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Geneva |
| Doctoral advisor | Marcel Guenin |
| Doctoral students | |
Jean-Pierre Eckmann (born 27 January 1944) is a mathematical physicist in the department of theoretical physics at the University of Geneva[1] and a pioneer of chaos theory and social network analysis.[2]
Eckmann is the son of mathematician Beno Eckmann.[3] He completed his Ph.D. in 1970 under the supervision of Marcel Guenin at the University of Geneva.[4] He has been a member of the Academia Europaea since 2001.[5] In 2012 he became a fellow of the American Mathematical Society.[6]
With Pierre Collet and Oscar Lanford, Eckmann was the first to find a rigorous mathematical argument for the universality of period-doubling bifurcations in dynamical systems, with scaling ratio given by the Feigenbaum constants.[7] In a highly cited 1985 review paper with David Ruelle,[8] he bridged the contributions of mathematicians and physicists to dynamical systems theory and ergodic theory,[9] put the varied work on dimension-like notions in these fields on a firm mathematical footing,[10] and formulated the Eckmann–Ruelle conjecture on the dimension of hyperbolic ergodic measures, "one of the main problems in the interface of dimension theory and dynamical systems".[11] A proof of the conjecture was finally published 14 years later, in 1999.[12] Eckmann has done additional mathematical work in very diverse fields such as statistical mechanics, partial differential equations, and graph theory.
His PhD students have included Viviane Baladi and Martin Hairer.[4]
References
- ^ Department member listing, Theoretical Physics, University of Geneva, retrieved 2011-04-29.
- ^ Barabási, Albert-László (2010), Bursts: the hidden pattern behind everything we do, Penguin, p. 87, ISBN 978-0-525-95160-5.
- ^ Profile for Jean-Pierre Eckmann on geni.com, retrieved 2011-04-30; Photo of Jean-Pierre Eckmann as a child with his parents, in the mathematical photo collection of the Mathematical Research Institute of Oberwolfach, retrieved 2011-04-30.
- ^ a b Jean-Pierre Eckmann at the Mathematics Genealogy Project
- ^ Academy of Europe: Eckmann Jean-Pierre, retrieved 2011-04-29; "New members of the Academia Europaea admitted 2001", The Tree: Newsletter of Academia Europaea (PDF), vol. 17, January 2002, p. 13.
- ^ List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
- ^ Hofstadter, Douglas R. (1996), Metamagical themas: questing for the essence of mind and pattern, Basic Books, pp. 382–383, ISBN 978-0-465-04566-2; Stewart, Ian (2002), Does God play dice?: the new mathematics of chaos (2nd ed.), Wiley-Blackwell, p. 189, ISBN 978-0-631-23251-3.
- ^ Eckmann, J.-P.; Ruelle, D. (1985), "Ergodic theory of chaos and strange attractors", Reviews of Modern Physics, 57 (3, part 1): 617–656, Bibcode:1985RvMP...57..617E, doi:10.1103/RevModPhys.57.617, MR 0800052.
- ^ Review of Eckmann & Ruelle (1985) by Charles Tresser in Mathematical Reviews, MR800052.
- ^ Review of Barreira, Pesin & Schmeling (1999) by Boris Hasselblatt in Mathematical Reviews, MR1709302.
- ^ Pesin, Yakov B. (1997), Dimension theory in dynamical systems: contemporary views and applications, Chicago lectures in mathematics, University of Chicago Press, p. 270, ISBN 978-0-226-66221-3.
- ^ Barreira, Luis; Pesin, Yakov; Schmeling, Jörg (1999), "Dimension and product structure of hyperbolic measures", Annals of Mathematics, 2nd ser., 149 (3): 755–783, doi:10.2307/121072, MR 1709302.
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