On automorphisms of quasi-circular domains fixing the origin

Abstract

It is known that automorphisms of quasi-circular domains fixing the origin are polynomial mappings. By introducing the so-called resonance order and quasi-resonance order, we provide a uniform upper bound for the degree of such polynomial automorphisms. As a particular consequence of our result, we obtain a generalization of the classical Cartan's theorem for circular domains to the quasi-circular case.

5 pages, to appear in Bull. Sci. Math

References in corpus (2)

• Automorphisms of normal quasi-circular domains
• On the linearity of origin-preserving automorphisms of quasi-circular domains in ${\mathbb{C}}^n$

Cited by in corpus (1)

• On the linearity of origin-preserving automorphisms of quasi-circular domains in ${\mathbb{C}}^n$