I am honored to introduce Professor David Ruelle's ``Poincare
His scientific carrier is remarkable for his various contributions and
for the conceptual continuity of the development through them. He has
been among the first to realize the relevance of a rigorous derivation
of the properties of equilibrium Statistical Mechanics as an essential
step towards understanding the theory of phase transitions. His
work has been an important guide to the scientists who in the sixties
were attempting accurate measurements of thermodynamic quantities,
like critical exponents, in various statistical mechanics models using
the newly available electronic computational tools in conjunction with
the use of rigorous results for assessing the correctness and
reliability of the computations.
The treatise on Statistical Mechanics, 1969, has become a classic book
and it is still the basis of the formation of the new generations of
scientists interested in the basic aspects of the theory. He has
written several other monographs which are widely known and used.
His critical work on the structure of Equilibrium Statistical
Mechanics led him to undertake in 1969 the analysis of the theory of
turbulence. The first publication on the subject was the epoch making
paper ``On the nature of turbulence'' in collaboration with
Takens. The paper criticized the theory of Landau, based on the
increasing complexity of quasi periodicity arising from successive
bifurcations in the Navier Stokes equations. The main idea that only
``generic'' behavior should be relevant was a strong innovation at the
time: this is amply proved by the hundreds of papers that followed on
the subject, theoretical, numerical and experimental.
The works making use of Ruelle's ideas stem also, and perhaps mainly,
from the innovative papers Ruelle wrote (and continues to write) after
the mentioned one. There he developed and strongly stressed the role
that dynamical systems ideas would be relevant and important in
understanding chaotic phenomena.
The impact on experimental works has been profound: one can say that
after the first checks were performed, some by notoriously skeptical
experimentalists, and produced the expected results we rapidly
achieved, by the end of the seventies, a stage in which the ``onset of
turbulence'' was so well understood that experiments dedicated to
check the so called ``Ruelle--Takens'' ideas on the onset of
turbulence were no longer worth being performed as one would know what
the result would be.
The very fact that a study of the onset of turbulence was physically
interesting was new at the time (the sixties). The ideas had been
independently worked out by Lorenz, earlier (in a 1963 paper): this
became clear almost immediately. However I think that Ruelle's view,
besides reviving the interest in Lorenz' work, which had not been
appreciated as it should have, were noticed by physicists and
mathematicians alike, and perhaps had more impact, because they were
more general and ambitious in scope and aimed at understanding from a
fundamental viewpoint a fundamental problem.
In 1973 he proposed that the probability distributions that describe
turbulence be what is now called the ``Sinai-Ruelle-Bowen''
distribution. This was developed in a sequence of many technical
papers and written explicitly only later in 1978. In my view this is
the most original contribution of Ruelle: it has not been well
understood for years although it has been quoted in impressively many
works on chaos. It had impact mostly on numerical works, but it
proposes a fundamental solution to one of the most outstanding
theoretical questions: what is the analog of the Boltzmann--Gibbs
distribution in non equilibrium statistical mechanics? his answer is a
general one valid for chaotic systems, be them gases of atoms
described by Newton's laws or fluids described by Navier Stokes
equations (or other fluid dynamics equations). Today the idea is still
a continuous source of works both theoretical and experimental.
Since the beginning of his work he has studied also problems
concerning other fields like operator theory and operator algebras
obtaining results remarkable for originality and depth: I mention here
only his results on the Lee--Yang theorem on the location of the zeros
of polynomials (a subject to which he continued to add new results and
applications) and the Haag--Ruelle theory of scattering in
relativistic quantum fields, very widely studied and applied, which is
still today virtually the only foundation for relativistic scattering
theory, employed in mathematical Physics, high energy phenomenology
and theoretical Physics.
In the last few years he has also provided important impulse to the
development of nonequilibrium statistical mechanics: his work
continues in this direction at the highest level. He has developed
foundational papers for the thery of nonequilibrium Thermodynamics
particularly with respect to the concept of entropy.
The work of Ruelle is of mathematical nature: but it is an example of how
important a conceptually rigorous and uncompromising approach can be
fruitful and lead to progress in very applied fields like experimental
fluid mechanics or numerical molecular dynamics simulations. His work is
in the tradition of the 1800's fundamental investigations in Physics.
His work, books and papers, is always very careful, clear and
polished: every word, however, is important and requires attention.
The awarding of the prize recognizes the cultural influence that he
has exercized in the last thirty years or so: and we are all here
united in this recognition.