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In this paper the adiabatic invariants for strongly nonlinear dynamical systems with two degrees of freedom described by complex functions are obtained. The method [1] developed for dynamical systems with one degree of freedom is extended to systems with two degrees of freedom. The method is based on Noether's theory and the use of Krylov-Bogolubov-Mitropolski (KBM) and elliptic-Krylov-Bogolubov (EKB) asymptotic techniques. The adiabatic invariants for two types of strong nonlinearities are constructed: the pure cubic nonlinearity and quasi-cubic nonlinearity. The adiabatic invariants are used to obtain the approximate solution to the equations of motion.

Adiabatic invariants for strongly nonlinear dynamical systems described with complex functions