We study the general chaotic features of dynamics of the phantom field modelled in terms of a single scalar field conformally coupled to gravity .
We demonstrate that the dynamics of the FRW model with dark energy in the form of phantom field can be regarded as a scattering process of two types : multiple chaotic and classical non-chaotic .
It depends whether the spontaneously symmetry breaking takes place .
In the first class of models with the spontaneously symmetry breaking the dynamics is similar to the Yang-Mills theory .
We find the evidence of a fractal structure in the phase space of initial conditions .
We observe similarities to the phenomenon of a multiple scattering process around the origin .
In turn the class of models without the spontaneously symmetry breaking can be described as the classical non-chaotic scattering process and the methods of symbolic dynamic are also used in this case .
We show that the phantom cosmology can be treated as a simple model with scattering of trajectories which character depends crucially on a sign of a square of mass .
We demonstrate that there is a possibility of chaotic behavior in the flat Universe with a conformally coupled phantom field in the system considered on non-zero energy level .
We obtain that the acceleration is a generic feature in the considered model without the spontaneously symmetry breaking .
We observe that the effective EOS coefficient oscillates and then approach to w = -1 .