Dynamics of quasi-parabolic one-resonant biholomorphisms

TL;DR

This paper investigates the dynamics of specific biholomorphic maps in complex space with one eigenvalue equal to one, establishing invariants and conditions for the existence of attracting regions.

Contribution

It introduces invariants and criteria for attracting domains in quasi-parabolic one-resonant biholomorphisms, advancing understanding of their complex dynamics.

Findings

Defined invariants for these biholomorphisms

Provided conditions for attracting domains

Enhanced understanding of complex dynamical behavior

Abstract

In this paper we study the dynamics of germs of quasi-parabolic one-resonant biholomorphisms of $\C^{n+1}$ fixing the origin, namely, those germs whose differential at the origin has one eigenvalue 1 and the others having a one dimensional family of resonant relations. We define some invariants and give conditions which ensure the existence of attracting domains for such maps.