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Characteristic exponents and invariant manifolds in Hilbert space
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…
Measures describing a turbulent flow
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…
On the Measures which describe turbulence
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…
Ergodic theory of differentiable dynamical systems
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…
