On the Measures which describe turbulence
TURBULENCE
HYDRODYNAMIQUE
THEORIE ASYMPTOTIQUE
HEURISTIQUE
Abstract : One expects that the average behavior (over large times) for hydordynamics and other natural phenomena is described by certain asymptotic measures on phase space. If initial conditions in a set of zero Lebesgu measure ar discarded, the asymptotic measures can be characterized on the basis of heuristic arguments. The requirement of stability under small stochastic perturbations produces measures with the same characterizations. We give here a critical discussion of the heuristic arguments and of the possible use of the characterizations of the asymptotic measures in the study of turbulence.
RUELLE
P/78/245
IHES
11/1978
A4
13 f.
EN
TEXTE
PREPUBLICATION
P_78_245.pdf
1978
Measures describing a turbulent flow
STABILITE
PERTURBATION
PROCESSUS STOCHASTIQUES
TEMPS
Abstract :Recent attempts at understanding hydrodynamic turbulence have used the ideas of strange attractors, characteristic exponents and stable manifolds for differentiable dynamical systems in finite dimensional spaces. This use was somewhat metophorical, because hydrodynamic evolution is defined in infinite dimensional functional spaces. A recent study indicates that many results in infinite dimensional Hilbert spaces under certain compactness assumptions. This is the case in particular for the time evolution defined by the Navier-Stokes equations in a bounded region of R2 or R3.
RUELLE
P/79/313
IHES
11/1979
A4
9 f.
EN
TEXTE
PREPUBLICATION
P_79_313.pdf
1979
Lyapunov exponents and Hodge theory
EXPOSANTS DE LIAPOUNOV
THEORIE DE HODGE
KONTSEVICH
ZORICH
M/97/13
IHES
01/1997
A4
9 f.
EN
TEXTE
PREPUBLICATION
M_97_13.pdf
1997
Ergodic theory of differentiable dynamical systems
THEORIE ERGODIQUE
SYSTEMES DYNAMIQUES
THEOREME
EXPOSANTS
VARIETES
STABILITE
Abstract : If f is a C1+? diffeomorphism of a compact manifold M, we prove the existence of stable manifolds, almost verywhere with respect to every f-invariant probability measure on M. These stable manifolds are smooth but do not in general constitute a continuous family. The proof of this stable manifold theorem (and similar results) is through the study of random matrix products (multiplicative ergodic theorem) and perturbation of such products.
RUELLE
P/78/240
IHES
09/1978
A4
31 f.
EN
TEXTE
PREPUBLICATION
P_78_240.pdf
1978
Conformal dynamical systems
SYSTEMES DYNAMIQUES
VARIETES
RADON
SCHISTE ARGILEUX
SULLIVAN
M/82/50
IHES
09/1982
A4
15 f.
EN
TEXTE
PREPUBLICATION
M_82_50.pdf
1982
Characteristic exponents and invariant manifolds in Hilbert space
THEORIE ERGODIQUE
MATHEMATIQUES
VARIETES
ESPACES DE HILBERT
THEOREMES
TOPOLOGIE
VALEURS PROPRES
FONCTIONS
SYSTEMES SYNAMIQUES
Abstract : The multiplicative ergodic theorem and the construction almost everywhere of stable and unstable manifolds (Pesin theory) are extended to differentiable dynamical systems on Hilbert manifolds under some compactness assumptions. The results apply to partial differential equations of evolution and also to non-invertible maps of compact manifolds.
RUELLE
P/80/11
IHES
03/1980
A4
38 f.
EN
TEXTE
PREPUBLICATION
P_80_11.pdf
1980