Quadratic polynomial automorphisms of dynamical degree golden ratio of \(\mathbb{C}^3\) (Q2730714)

The study of the dynamics of polynomial diffeomorphisms of \({\mathbb C}^n\) was started by \textit{E. Bedford} and \textit{J. Smillie} [Invent. Math. 103, 69-99 (1991; Zbl 0721.58037)].NEWLINENEWLINENEWLINEIn the paper under review, the author studies the dynamics of quadratic shift-like polynomial automorphisms of \({\mathbb C}^3\) of the form NEWLINE\[NEWLINEf(x,y,z)=(y,z,yz+by+cz+dx+e),\quad d\neq 0.NEWLINE\]NEWLINE The existence of Green functions \(G^{\pm}(x,y,z)\) associated to the dynamical degree \(d(f)\) is proved by using filtration property. They are continuous and plurisubharmonic on \({\mathbb C}^3\).NEWLINENEWLINENEWLINEAs applications, some properties of the set of zero points of a Green function and its complement are given.