On continuous dynamics of automorphisms of \(\mathbb{C}^ 2\) (Q1313298)

The author studies one-parameter subgroups of the group of polynomial automorphisms of \(\mathbb{C}^ 2\) and of the shear group of \(\mathbb{C}^ 2\) defined by \textit{J.-P. Rosay} and \textit{W. Rudin} [Trans. Am. Math. Soc. 310, No. 1, 47-86 (1988; Zbl 0708.58003)]. It is shown that such a subgroup is conjugate to a one-parameter group in the group of all affine transformations of \(\mathbb{C}^ 2\) or in the group of elementary automorphisms of the group of polynomial automorphisms of \(\mathbb{C}^ 2\). As an application one obtains some results about the asymptotic behaviour of one-parameter subgroups in each of these two settings.