We study the behavior of orbits in a galactic dynamical model composed of an harmonic core and a strong bar potential. Numerical calculations suggest that low angular momentun orbits display chaotic motion. The area on the x-px phase plane covered by chaotic orbits increases as the angular velocity of the system increases or the strength of the harmonic term decreases. The S(c) spectrum is introduced and used to detect the island motion and study the evolution of the sticky regions. Comparison with previous work is also made revealing the leading role of the new spectrum.