ON THE CHANGE IN THE POWER OF THE SPECTRUM OF THE EXACT AND ABSOLUTE WANDERING EXPONENT DURING THE TRANSITION FROM A TWO-DIMENSIONAL NONLINEAR SYSTEM TO A SYSTEM OF ITS FIRST APPROXIMATION

The sets of values (spectra) of the wandering exponents of solutions of differential systems are studied. Two-dimensional systems with nonlinearity of an arbitrarily specified higher order of smallness in the neighborhood of the origin are constructed, for which all solutions are infinitely extendable to the right and any of the spectra of their wandering exponents can coincide with both the segment [0, 1] and with any pre-specified non-empty subset of rational numbers of this segment, while the spectra of linear systems of their first approximation consist of only one element. Moreover, the spectra of the exponents of the original system coincide with the corresponding spectra of the wandering exponents of the narrowing of the constructed nonlinear two-dimensional systems to the direct product of any open neighborhood of the zero of the phase plane and the time semi-axis.