Institut des Hautes Études Scientifiques

About: Institut des Hautes Études Scientifiques is a facility organization based out in Bures-sur-Yvette, France. It is known for research contribution in the topics: Gravitational wave & Gauge theory. The organization has 715 authors who have published 2293 publications receiving 155939 citations. The organization is also known as: Institute of Advanced Scientific Studies & Institut des Hautes Études Scientifiques.

Ergodic theory of chaos and strange attractors

Abstract: Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the geometric theory of differentiable dynamical systems, moderately excited chaotic systems require new tools, which are provided by the ergodic theory of dynamical systems. This theory has reached a stage where fruitful contact and exchange with physical experiments has become widespread. The present review is an account of the main mathematical ideas and their concrete implementation in analyzing experiments. The main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions). The relations between these quantities, as well as their experimental determination, are discussed. The systematic investigation of these quantities provides us for the first time with a reasonable understanding of dynamical systems, excited well beyond the quasiperiodic regimes. This is another step towards understanding highly turbulent fluids.

Recurrence Plots of Dynamical Systems

Abstract: A new graphical tool for measuring the time constancy of dynamical systems is presented and illustrated with typical examples.

La conjecture de Weil I.

Abstract: © Publications mathematiques de l’I.H.E.S., 1974, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www. ihes.fr/IHES/Publications/Publications.html), implique l’accord avec les conditions generales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systematique est constitutive d’une infraction penale. Toute copie ou impression de ce fichier doit contenir la presente mention de copyright.

Pseudo holomorphic curves in symplectic manifolds

Abstract: Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called a (non-parametrized) J-curve in V. A curve C C V is called closed if it can be (holomorphically !) parametrized by a closed surface S. We call C regular if there is a parametrization f : S ~ V which is a smooth proper embedding. A curve is called rational if one can choose S diffeomorphic to the sphere S 2.