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
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
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
The Multiplicative ergodic theorem
THEORIE ERGODIQUE
SYSTEMES DYNAMIQUES
DYNAMIQUE DIFFERENTIABLE
RUELLE
P/78/214
IHES
03/1978
A4
12 f.
EN
TEXTE
PREPUBLICATION
P_78_214.pdf
1978
Analiticity properties of the characteristic exponents of random matrix products
EXPOSANTS
MATRICES
RUELLE
P/77/193
IHES
11/1977
A4
11 f.
EN
TEXTE
PREPUBLICATION
P_77_193.pdf
1977
Sensitive dependence on initial conditions and turbulent behavior of dynamical systems
SYSTEMES DYNAMIQUES
DYNAMIQUE DIFFERENTIABLE
Abstract : The asymptotic behavior of differentiable dynamical systems is analyzed. We discuss its descriptoin by asymptotic measures and the turbulent behavior with senditive dependence on initial condition.
RUELLE
P/77/190
IHES
10/1977
A4
9 f.
EN
TEXTE
PREPUBLICATION
P_77_190.pdf
1977