Plurisubharmonic Lyapunov functions
type: Item
instance of: scholarly article
title: Plurisubharmonic Lyapunov functions
zbMATH Open document ID: 1065.37014
author: Małgorzata Stawiska
published in: Michigan Mathematical Journal
publication date: 2004-11-11T00:00:00Z
review text: Suppose the holomorphic map \(f: \mathbb{C}\mathbb{P}^2\to \mathbb{C}\mathbb{P}^2\) has an invariant nonsingular quadratic curve \(A\) contained in the critical set of. The author proves that the pluricomplex Green function \(G_K\) for the repeller \(K\) dual to \(A\), with logarithmic pole along \(A\), is a PSH Lyapunov function for \(f\) in \(\mathbb{C}\mathbb{P}^2\setminus(A\cup f^{-1}(A))\). Her main result is the following theorem: \(G_K\) is a continuous plurisubharmonic function satisfying \(G_K\leq G_K\circ f\) in \(\mathbb{C}\mathbb{P}^2\setminus (A\cup f^{-1}(A))\).
reviewed by: Jianyong Qiao
Mathematics Subject Classification ID: 37B25
Mathematics Subject Classification ID: 32U35
Mathematics Subject Classification ID: 37F10
zbMATH DE Number: 2114460
zbMATH Keywords: holomorphic dynamics
zbMATH Keywords: Lyapunov function
zbMATH Keywords: repelling set
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1080837739
OpenAlex ID: W2003522688
cites work: Q3135846
cites work: Q4797607
cites work: The Dirichlet problem for a complex Monge-Ampère equation
cites work: A new capacity for plurisubharmonic functions
cites work: Plurisubharmonic functions with logarithmic singularities
cites work: Hypersurfaces exceptionnelles des endomorphismes de ??(n)
cites work: Q4180600
cites work: Mesures de Monge-Ampère et mesures pluriharmoniques. (Monge-Ampère measures and pluriharmonic measures)
cites work: Q4474935
cites work: Q4310116
cites work: Q5571530
cites work: Q3993500
cites work: Q4301007
cites work: Q4002495
cites work: Metrics Associated with Extremal Plurisubharmonic Functions
cites work: Q3999267
cites work: Q4302493
cites work: Domaines pseudoconvexes infinis et la métrique riemannienne dans un espace projectif
cites work: Fatou sets in complex dynamics on projective spaces
cites work: Fonction de Green pluriclomplexe à pole à l'infini sur un espace de Stein parabolique et applications.
DOI: 10.1307/MMJ/1080837739
description: scientific article; zbMATH DE number 2114460