Summary: First-order approximate first integrals (conserved quantities) of a Hamiltonian dynamical system with two degrees of freedom which arises in the modeling of central part of a deformed galaxy are obtained based on the approximate Noether symmetries for resonances \(\omega_1 =\omega_2\), \(\omega_1= 2\omega_2\) and \(2\omega_1= 3\omega_2\). Furthermore, KAM curves are obtained analytically and compared with numerical curves on the Poincaré surface of section.