Abstract: This paper is assigned to discuss the dynamics of a special class of polynomial automorphisms of C which was shown to be dense in the group of the polynomial automorphisms.We give some results about the analytic and geometric properties of the filled-in Julia set and the nonwandering set.We also make a characterization of the stable and unstable manifold for the filled-in Julia set.Furthermore,the number of the fixed points for such maps is studied.

Key words: dynamics, fikked-in Julia set, nonwandering set