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Local Lyapunov exponents and a local estimate of Hausdorff dimension. (English) Zbl 0684.58022
Summary: The Lyapunov dimension has already been used to give estimates of the Hausdorff dimension of an attractor associated with a dissipative ODE or PDE. Here we give a slightly different version, utilizing local Lyapunov exponents, in particular we show the existence of a critical path along which the Hausdorff dimension is majorized by the associated Lyapunov dimension. This result is then applied to Lorenz equations to deduce a better estimate of the dimension of the universal attractor. We conclude with an example that shows some of the drawbacks of this estimate.

37C70 Attractors and repellers of smooth dynamical systems and their topological structure
28A75 Length, area, volume, other geometric measure theory
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