  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 $w=-1$.
