Jean-Pierre Eckmann (born 27 January 1944) is a Swiss

mathematical physicist Mathematical physics refers to the development of mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developmen ...

in the department of

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experi ...

at the

University of Geneva The University of Geneva (French: ''Université de Genève'') is a public research university located in Geneva, Switzerland. It was founded in 1559 by John Calvin as a theological seminary. It remained focused on theology until the 17th centur ...

and a pioneer of

chaos theory Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have ...

and

social network analysis Social network analysis (SNA) is the process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of ''nodes'' (individual actors, people, or things within the network) ...

.. Eckmann is the son of mathematician

Beno Eckmann Beno Eckmann (31 March 1917 – 25 November 2008) was a Swiss mathematician who made contributions to algebraic topology, homological algebra, group theory, and differential geometry. Life Born in Bern, Eckmann received his master's degree fro ...

. He completed his PhD in 1970 under the supervision of Marcel Guenin at the University of Geneva. He has been a member of the

Academia Europaea The Academia Europaea is a pan-European Academy of Humanities, Letters, Law, and Sciences. The Academia was founded in 1988 as a functioning Europe-wide Academy that encompasses all fields of scholarly inquiry. It acts as co-ordinator of Europea ...

since 2001. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...

. He is also a member of the

Göttingen Academy of Sciences and Humanities The Göttingen Academy of Sciences (german: Akademie der Wissenschaften zu Göttingen)Note that the German ''Wissenschaft'' has a wider meaning than the English "Science", and includes Social sciences and Humanities. is the second oldest of the se ...

. With

Pierre Collet Pierre Collet (10 March 1914 – 30 October 1977) was a French film actor. He appeared in more than 100 films and television shows between 1943 and 1977. Selected filmography * ''Goodbye Leonard'' (1943) - Le marchand d'habits (uncredite ...

and Oscar Lanford, Eckmann was the first to find a rigorous mathematical argument for the universality of

period-doubling bifurcation In dynamical systems theory, a period-doubling bifurcation occurs when a slight change in a system's parameters causes a new periodic trajectory to emerge from an existing periodic trajectory—the new one having double the period of the original. W ...

s in

dynamical systems In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...

, with scaling ratio given by the

Feigenbaum constants In mathematics, specifically bifurcation theory, the Feigenbaum constants are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map. They are named after the physicist Mitchell J. Feigenbaum. Histo ...

. In a highly cited 1985 review paper with

David Ruelle David Pierre Ruelle (; born 20 August 1935) is a Belgian mathematical physicist, naturalized French. He has worked on statistical physics and dynamical systems. With Floris Takens, Ruelle coined the term ''strange attractor'', and developed a ...

, he bridged the contributions of mathematicians and physicists to

dynamical systems theory Dynamical systems theory is an area of mathematics used to describe the behavior of complex systems, complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theo ...

and

ergodic theory Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...

, put the varied work on dimension-like notions in these fields on a firm mathematical footing, and formulated the Eckmann–Ruelle conjecture on the dimension of hyperbolic ergodic measures, "one of the main problems in the interface of

dimension theory In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordi ...

and dynamical systems". A proof of the conjecture was finally published 14 years later, in 1999.. Eckmann has done additional mathematical work in very diverse fields such as statistical mechanics,

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

, and

graph theory In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

. His PhD students have included

Viviane Baladi Viviane Baladi (born 23 May 1963) is a mathematician who works as a director of research at the Centre national de la recherche scientifique (CNRS) in France. Originally Swiss, she has become a naturalized citizen of France.. Her research concern ...

, and

Martin Hairer Sir Martin Hairer (born 14 November 1975) is an Austrian-British mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. He is Professor of Mathematics at EPFL (École Polytechnique F ...

References

External links

Website of Jean-Pierre Eckmann
1944 births Living people Mathematical physicists University of Geneva alumni University of Geneva faculty Fellows of the American Mathematical Society {{mathematician-stub