Local estimates for the Hausdorff dimension of an attractor (Q750985)

In the paper a continuous nonlinear semigroup acting on a separable Hilbert space is considered. It is assumed that the semigroup admits a compact global attractor on which it is bijective. In this context local and global Lyapunov exponents are defined and used to introduce the Douady-Oesterlé dimension. It is shown the existence of a critical path in the attractor for which the local Douady-Oesterlé dimension dominates the Hausdorff dimension of the attractor. An example for a Lorenz type equation is given.