Small random perturbations of dynamical systems and the definition of attractors
RESEAUX
SYSTEMES DYNAMIQUES
PHYSIQUE STATISTIQUE
SYSTEMES COMPLEXES
THEORIES NON LINEAIRES
Abstract : The strange attractors plotted by computers and seen in physical experiments do not necessarily have an open basin of attraction. In view of this we study a new definition of attractors based on ideas of Conley. We argue that the attractors observed in the presence of small random perturbations correspond to this new definition.
RUELLE
P/81/23
IHES
03/1981
A4
15 f.
EN
TEXTE
PREPUBLICATION
P_81_23.pdf
1981
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