Polynomial Diffeomorphisms of $\C^2$. VIII: Quasi-Expansion

TL;DR

This paper explores a new dynamical property called quasi-expansion for polynomial diffeomorphisms of , extending hyperbolic concepts to higher dimensions and broadening understanding of complex dynamical systems.

Contribution

It introduces the concept of quasi-expansion, a generalization of hyperbolicity, for polynomial diffeomorphisms of , advancing the theoretical framework of complex dynamics.

Findings

Defines quasi-expansion as a new dynamical property

Generalizes hyperbolicity to higher-dimensional polynomial maps

Provides foundational insights for future research in complex dynamics

Abstract

This paper continues our investigation of the dynamics of polynomial diffeomorphisms of C^2. We introduce a dynamical property of polynomial diffeomorphisms that generalizes hyperbolicity in the way that semi-hyperbolicity generalizes hyperbolicity for polynomial maps of the complex plane.