A generalization of Siegmund's normal forms theorem to systems with \(\mu \)-dichotomies (Q6616065)

In the framework of Carathéodory differential equations, \textit{S. Siegmund} [J. Differ. Equations 178, No. 2, 541--573 (2002; Zbl 1011.34027)] extended Poincaré's classical normal form theory to the time-variant case. Here, suitable extensions of the non-resonance conditions were formulated in terms of the dichotomy spectrum for the linearization. \N\NThe interesting paper at hand establishes a corresponding normal form reduction technique based on the more general concept of \(\mu\)-dichotomies established in [\textit{C. M. Silva}, J. Differ. Equations 375, 618--652 (2023; Zbl 1529.34055)] and its associated spectrum.