LIE TRANSFORMATION METHOD FOR DYNAMICAL-SYSTEMS HAVING CHAOTIC BEHAVIOR

The paper presents recent developments in a singular perturbation meth od, known as the ''Lie transformation method'' for the analysis of non linear dynamical systems having chaotic behavior. A general approximat e solution for a system of first-order differential equations having a lgebraic nonlinearities is introduced. Past applications to simple dyn amical nonlinear models have shown that this method yields highly accu rate solutions of the systems. In the present paper the capability of this method is extended to the analysis of dynamical systems having ch aotic behavior: indeed, the presence of ''small divisors'' in the gene ral expression of the solution suggests a modification of the method t hat is necessary in order to analyze nonlinear systems having chaotic behavior (indeed, even non-simple-harmonic behavior). For the case of Hamiltonian systems this is consistent with the KAM (Kolmogorov-Arnold -Moser) theory, which gives the limits of integrability for such syste ms; in contrast to the KAM theory, the present formulation is not limi ted to conservative systems. Applications to a classic aeroelastic pro blem (panel flutter) are also included.