| Abstract: |
| The multiplicative ergodic theorem (the Oseledets theorem), the Folquet theorem and exponential separation are related results concerning the decomposition of the phase space (more generally, of fiber bundles) on which a dynamical system acts. This decomposition is based on the system`s dynamics and exponential growth rates (Lyapunov exponents). Sometimes, when the dynamical system arises from differential equations, it may happen that after some time the associated mappings transfer elements from a Banach space $X$ into a (better) space $Y$, continuously embedded in the former. This occurs, for instance, in parabolic problems, in which an irregular initial condition becomes a smooth function, or for delay differential equations, in which an initial function of class $L_p$ becomes, after some time, continuous (and even absolutely continuous, hence differentiable almost everywhere). We will show that, on the embedded space, the dynamics of the system remains the same |
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