  Motivated to explore the dynamical mechanism of multi-fragmentation phase
transition and expand our knowledge on the deterministic chaos in nonlinear
dynamic process, we study systematically the nonlinear dynamical behaviors of
heavy ion collisions at intermediate energy. In order to highlight the general
characteristics of the collision dynamics, in the present paper, we simulate a
simple collision system, $Ca+Ca$, and obverse the performances of the typical
nonlinear characteristic quantities such as the production of generalized
entropy and the fractal structure of the semiclassical phase space during the
reaction process. The multifragmentation entropy, information dimension and the
dynamical fluctuations of fragment mass distribution in the final state of the
reaction are also evaluated. Our results about the intermediate processes and
the final products of the reaction are verified mutually so that confirm
strongly the existence of nonlinear chaos in the heavy ion collisions at
intermediate energy. Meanwhile, we find that the typical characteristics of the
critical phase transition obtained in the analysis of the final production of
the reaction are relatively more clear in the vicinity of the incident energies
$E=100 MeV$.
