  The dynamical behaviour of near by trajectories is being estimated by
Lyapunov Characteristic Exponents(LCEs) in the Generalized Photogravitational
Chermnykh-Like problem. It is found that the trajectories of the Lagrangian
point $L_4$ move along the epicycloid path, and spirally depart from the
vicinity of the point. The LCEs remain positive for all the cases and depend on
the initial deviation vector as well as renormalization time step. It is
noticed that the trajectories are chaotic in nature and the $L_4$ is
asymptotically stable. The effects of radiation pressure, oblateness and mass
of the belt are also examined in the present model.
