## Arbitrarily accurate approximate inertial manifolds of fixed dimension.(English)Zbl 1052.34509

Summary: By employing an embedding result due to Ma\=né, and its recent strengthening due to Foias and Olson it is shown that a global attractor with finite fractal (box counting) dimension $$d$$ lies within an arbitrarily small neighbourhood of a smooth graph over the space spanned by the first $$2d+1$$ Fourier-Galerkin modes. The proof is, however, nonconstructive.

### MSC:

 34G20 Nonlinear differential equations in abstract spaces 34D45 Attractors of solutions to ordinary differential equations 47H20 Semigroups of nonlinear operators
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### References:

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