Jean-Pierre Eckmann
Encyclopedia
Jean-Pierre Eckmann is a mathematical physicist in the department of theoretical physics at the University of Geneva
and a pioneer of chaos theory
and social network analysis
.
Eckmann is the son of mathematician Beno Eckmann
. He completed his Ph.D. in 1970 under the supervision of Marcel Guenin at the University of Geneva. He has been a member of the Academia Europaea
since 2001.
With Pierre Collet and H. Koch, Eckmann was the first to find a rigorous mathematical argument for the universality
of period-doubling bifurcation
s in dynamical systems, with scaling ratio given by the Feigenbaum constants
. In a highly cited 1985 review paper with David Ruelle
, he bridged the contributions of mathematicians and physicists to dynamical systems theory
and ergodic theory
, 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
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, and graph theory
.
Martin Hairer
was one of his PhD students.
University of Geneva
The University of Geneva is a public research university located in Geneva, Switzerland.It was founded in 1559 by John Calvin, as a theological seminary and law school. It remained focused on theology until the 17th century, when it became a center for Enlightenment scholarship. In 1873, it...
and a pioneer of chaos theory
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
and social network analysis
Social network
A social network is a social structure made up of individuals called "nodes", which are tied by one or more specific types of interdependency, such as friendship, kinship, common interest, financial exchange, dislike, sexual relationships, or relationships of beliefs, knowledge or prestige.Social...
.
Eckmann is the son of mathematician Beno Eckmann
Beno Eckmann
Beno Eckmann was a Swiss mathematician who was a student of Heinz Hopf.Born in Bern, Eckmann received his master's degree from Eidgenössische Technische Hochschule Zürich in 1931. Later he studied there under Heinz Hopf, obtaining his Ph.D. in 1941...
. He completed his Ph.D. in 1970 under the supervision of Marcel Guenin at the University of Geneva. He has been a member of the Academia Europaea
Academia Europaea
Academia Europæa is a European non-governmental scientific academy founded in 1988. Its members are scientists and scholars who collectively aim to promote learning, education and research. It publishes European Review through Cambridge Journals....
since 2001.
With Pierre Collet and H. Koch, Eckmann was the first to find a rigorous mathematical argument for the universality
Universality (dynamical systems)
In statistical mechanics, universality is the observation that there are properties for a large class of systems that are independent of the dynamical details of the system. Systems display universality in a scaling limit, when a large number of interacting parts come together...
of period-doubling bifurcation
Period-doubling bifurcation
In mathematics, a period doubling bifurcation in a discrete dynamical system is a bifurcation in which the system switches to a new behavior with twice the period of the original system...
s in dynamical systems, with scaling ratio given by the Feigenbaum constants
Feigenbaum constants
The Feigenbaum constants are two mathematical constants named after the mathematician Mitchell Feigenbaum. Both express ratios in a bifurcation diagram.The first Feigenbaum constant ,...
. In a highly cited 1985 review paper with David Ruelle
David Ruelle
David Pierre Ruelle is a Belgian-French mathematical physicist. He has worked on statistical physics and dynamical systems. With Floris Takens he coined the term strange attractor, and founded a new theory of turbulence...
, he bridged the contributions of mathematicians and physicists to dynamical systems theory
Dynamical systems theory
Dynamical systems theory is an area of applied mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. When difference...
and ergodic theory
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
, 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
Dimension theory
In mathematics, dimension theory is a branch of general topology dealing with dimensional invariants of topological spaces.-See also:*Lebesgue covering dimension*Inductive dimensions *Dimension...
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
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
, partial differential equations, and graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
.
Martin Hairer
Martin Hairer
Martin Hairer is a mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations....
was one of his PhD students.