Filtrations and Polynomial Mappings in Cⁿ

In some sense, the filtration property is the easiest property of the Hénon map. It is the most fundamental of the tools we have. When n > 2, the group of polynomial automorphisms of Cⁿ is not at all understood. (The paper of Friedland-Milnor made essential use of the Theorem of Jung on the structure of the polynomial automorphisms of C².) However, there is the class of regular automorphisms which can be approached following the general approach used for the Hénon family. Shafikov and Wolf have shown that some of the theory can be carried over to higher dimension.

Filtrations for the Fibonacci Map