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Bohl dichotomy is a notion of hyperbolicity for linear nonautonomousdifference equations that is weaker than the classical concept of exponentialdichotomy. In the class of systems with bounded invertible coefficient matriceswhich have bounded inverses, we study the relation between the set$\mathrm{BD}$ of systems with Bohl dichotomy and the set $\mathrm{ED}$ ofsystems with exponential dichotomy. It can be easily seen from the definitionof Bohl dichotomy that $\mathrm{ED} \subseteq \mathrm{BD}$. Using acounterexample we show that the closure of $\mathrm{ED}$ is not contained in$\mathrm{BD}$. The main result of this paper is the characterization$\operatorname{int}\mathrm{BD} = \mathrm{ED}$. The proof uses upper triangularnormal forms of systems which are dynamically equivalent and utilizes adiagonal argument to choose subsequences of perturbations each of which isconstructed with the Millionshikov Rotation Method. An Appendix describes theMillionshikov Rotation Method in the context of nonautonomous differenceequations as a universal tool.

The new notion of Bohl dichotomy for nonautonomous difference equations and its relation to exponential dichotomy