Asymptotic decomposition of systems of nonlinear ordinary differential equations (Q797750)

The construction of solutions of non linear ODE's by meams of asymptotic expansions relies on a relative-magnitude ordering of terms in the ODE's. This is most easily accomplished with the help of a 'small parameter'. Since usual small parameter expansions are not always successful, an alternate construction method is proposed. It relies on a special operator decomposition, in principle independent of any small parameter. Potential success is expected from the use of a variant of the 'similarity principle', the presence of similarity being associated with the presence of a transformation group. An operator decomposition with averaging scheme is worked out in terms of Lie series. The publication of a ''correctness''-proof is announced. The single illustrative example (Van der Pol equation) gives the impression that the scheme is quite laborious and cumbersome. Whether it provides a wider application the scope remains to be seen.