Linearization of Hénon maps with resonant eigenvalues at an attracting fixed point
The paper under review deals with the problem of local holomorphic linearization of attracting Hénon maps in $\mathbb{C}^2$ at a fixed point. It is well known that if there are no resonances between the eigenvalues of the linear part then holomorphic linearization is always possible. The author addresses the question of whether the presence of resonances does always prevent holomorphic linearization. He provides explicit examples of Hénon maps of arbitrary degree $d\ge 3$ which, despite having resonances, are holomorphically linearizable. In the case of Hénon maps of degree $d=2$, he proves that resonances of order $k=2, 3, 4, 5, 6$ always prevent holomorphic linearization and presents examples of maps with resonances of degree $k=7, 8, 9, 10, 11, 12$ which are linearizable.
scientific article; zbMATH DE number 6837886
scientific article