Attracting basins in \({\mathbb{P}}^2\)
type: Item
instance of: scholarly article
title: Attracting basins in \({\mathbb{P}}^2\)
zbMATH Open document ID: 0982.37044
DOI: 10.1007/BF02921795
author: Estela Ana Gavosto
published in: The Journal of Geometric Analysis
publication date: 2000-06-22T00:00:00Z
review text: The paper is devoted to the dynamics of holomorphic mappings in \(\mathbb{P}^2\). It is known that, even in \(\mathbb{C}^2\), the dynamics is quite different and richer than in \(\mathbb{C}\). However in \(\mathbb{P}^2\) (projective space) the picture (dynamics) is different. Namely, the author shows that the dynamics of holomorphic mappings in \(\mathbb{P}^2\) can have many attracting basins. Moreover she shows that if a family of mappings has a complex generic homoclinic tangency, then some of the mappings in the family have an attractive periodic fixed point.
Mathematics Subject Classification ID: 37F45
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 37G25
zbMATH DE Number: 1463791
zbMATH Keywords: holomorphic dynamics
zbMATH Keywords: projective space
zbMATH Keywords: attracting basins
zbMATH Keywords: periodic fixed point
zbMATH Keywords: homoclinic tangency
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02921795
OpenAlex ID: W1997355452
description: scientific article; zbMATH DE number 1463791