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Upper bound for the Hausdorff dimension of invariant sets of evolution variational inequalities

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Abstract

We consider the method of determining observations for obtaining an upper bound for the fractal dimension and the Hausdorff dimension of invariant sets of variational inequalities. We suggest a process for constructing determining observations, in particular, for dissipativity, with the use of frequency theorems for evolution systems (the Likhtarnikov–Yakubovich theorem). As an example, we consider a viscoelasticity problem in mechanics.

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  1. St. Petersburg State University, St. Petersburg, Russia

    A. V. Kruck

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  1. A. V. Kruck
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Kruck, A.V. Upper bound for the Hausdorff dimension of invariant sets of evolution variational inequalities. Diff Equat 51, 1703–1716 (2015). https://doi.org/10.1134/S0012266115130042

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  • DOI: https://doi.org/10.1134/S0012266115130042

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