Upper Bound for the Hausdorff Dimension of Invariant Sets of Evolution Variational Inequalities

摘要

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.