| Abstract: |
| We provide a unifying framework for the construction of exponential attractors for infinite dimensional dynamical
systems that allows us to generalize, improve and compare existing methods that are commonly used to
construct exponential attractors. For autonomous deterministic systems we formulate necessary and sufficient
conditions for the existence of discrete exponential attractors in terms of a covering condition for iterates of the
absorbing set under the time evolution of the semigroup. The parameters in the covering condition determine
the estimate for the fractal dimension of the exponential attractor and the exponential rate of attraction. We
then verify the covering condition for existing approaches to construct exponential attractors where the most
general setting concerns quasi-stable semigroups in complete metric spaces. Generalizing previous notions and
methods used in the literature on exponential attractors then allows us to compare widely used approaches. To
conclude, we mention generalizations of the constructions for non-autonomous and random dynamical systems. |
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