# Jean-Pierre Eckmann

**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]

Jean-Pierre Eckmann | |
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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 |

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] He is also a member of the Göttingen Academy of Sciences and Humanities.[7]

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.[8] In a highly cited 1985 review paper with David Ruelle,[9] he bridged the contributions of mathematicians and physicists to dynamical systems theory and ergodic theory,[10] put the varied work on dimension-like notions in these fields on a firm mathematical footing,[11] 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".[12] A proof of the conjecture was finally published 14 years later, in 1999.[13] 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, Pierre Collet, 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.
- 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),**17**, January 2002, p. 13, archived from the original (PDF) on 9 August 2011. - List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
- "Members: Göttingen Academy of Sciences and Humanities (AdW)".
*adw-goe.de*. Retrieved 4 September 2018. - 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, arXiv:math/9905205, doi:10.2307/121072, MR 1709302.