Invariants of multi-parameter approximate transformation groups

The problem of finding all functionally independent invariants for a given multi-parameter approximate transformation group is considered. The criterion for approximate function to be invariant under an approximate transformation group is similar to that of Lie’s theory and is based on operators of the corresponding approximate Lie algebra. The calculation of invariants of an approximate transformation group reduces to solving the system of linear nonhomogeneous first-order PDEs. The sufficient conditions of compatibility and completeness for these systems are proved.  2003 Elsevier Science (USA). All rights reserved