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
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
Asymptotic invariants of infinite groups
GROUPES INFINIS
INVARIANTS
DEVELOPPEMENTS ASYMPTOTIQUES
GROMOV
M/92/08
IHES
A4
100 f.
EN
TEXTE
PREPUBLICATION
M_92_08.pdf
1992