For nonautonomous linear difference systems, the paper introduces a new intermediate dichotomy spectrum, proposes a conjecture for its structure, and gives a counterexample showing the nonuniform exponential dichotomy spectrum is not preserved under weak kinematic similarity.
A.: Spectrum invariance dilemma for nonuniformly kinematically similar sys- tems
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Discrete $\mu$-dichotomy spectrum: beyond uniformity and new insights
For nonautonomous linear difference systems, the paper introduces a new intermediate dichotomy spectrum, proposes a conjecture for its structure, and gives a counterexample showing the nonuniform exponential dichotomy spectrum is not preserved under weak kinematic similarity.