Some co-tame automorphisms of affine spaces

The investigation of co-tame automorphisms of the affine space A(k)(n) is helpful to understand the structure of its automorphisms group. In this paper, we show the co-tameness of several classes of automorphisms, including some 3-parabolic automorphisms, powerlinear automorphisms, homogeneous automorphisms in small dimension or small transcendence degree. We also classify all additive-nilpotent automorphisms in dimension four and show that they are co-tame.