Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · math/0309253

Invariant Nonrecurrent Fatou Components of Automorphisms of $C^2$

Daniel Jupiter·Krastio Lilov
View original source ↗Read source document ↗Export metadata ↓

Abstract

We examine invariant nonrecurrent Fatou components of automorphisms of $\mathbb{C}^2$ in the case where all limit maps are constant. We show that except in special cases there cannot be more than one such limit map. We also briefly examine such Fatou components where the limit maps may be nonconstant. Lastly we present a few examples of such Fatou components.

Explore related subjects

math.CVmath.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Daniel Jupiter, Krastio Lilov. 2003-09-16. Invariant Nonrecurrent Fatou Components of Automorphisms of $C^2$. https://arxiv.org/abs/math/0309253

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Different approach to certain problems in univalent function theory

Using different approach we consider some problems for the class $\mathcal{S}_{ex}^{\star}$ defined by the condition $\frac{zf'(z)}{f(z)}\prec e^{αz}$, $0<α\leq1.$ Our method is more simple than that used by Das and Sarkar in their work: \textit{Sharp coefficient estimates for the exponential starlike class $S^\star_{ex}$} (\cite{DS26}).

math.CV↗
arXiv2026

Local convexity obstructions for bounded realizations of Teichmüller space

Let $D\subset\mathbb{C}^n$, $n\ge2$, be a bounded domain that is biholomorphic to a finite-dimensional Teichmüller space. We prove that $\partial D$ has no locally convex boundary patch containing a complex $(n-1)$-dimensional manifold through each of its points. Note that in complex dimension two this excludes every locally convex boundary point, without any boundary regularity assumption. In every dimension, we also exclude locally convex $C^2$ boundary patches.

math.CV↗