Counting uniformly attracting solutions of nonautonomous differential equations

Bounded uniform attractors and repellors are the natural nonautonomous analogues of autonomous stable and unstable equilibria. Unlike for equilibria, it is generally a difficult dynamical task to determine the number of uniformly attracting or repelling solutions for a given nonautonomous equation, even if the latter exhibits strong structural properties such as e.g. polynomial growth in space or periodicity in time. The present note highlights this aspect by proving that the number of uniform attractors is locally finite for several classes of equations, and by providing examples for which this number can be any $N\in \N$. These results and examples extend and complement recent work on nonautonomous differential equations.