Approximate first integrals of a Hamiltonian system with two-degrees of freedom

Abstract

Approximate Noether symmetries of a Hamiltonian system with two-degrees of freedom have been determined by incorporating the resonances. Approximate first integrals corresponding to these symmetries have been obtained by utilizing the approximate version of the Noether's theorem. Analytically obtained result has been compared with the numerically obtained Poincaré's surface of sections.