Asymptotic decomposition of completely integrable Pfaffian systems with small parameter
The method of asymptotic decomposition is extended to systems of the form \((1)\quad dx=(\Omega (x)+\epsilon {\tilde \Omega}(\epsilon,x))dt,\) \(x(t_ 0)=x_ 0\) where x is an n-dimensional vector and t is an m- dimensional vector. The system (1) is considered completely integrable. The authors introduce transformations which map the system (1) onto the differential system for slow variables and a differential system for fast variables. The system for slow variables can be solved separately and the system for fast variables can be then solved by quadratures. Further, the properties of the corresponding operators are analyzed.
scientific article; zbMATH DE number 4148599