Attracting basins in \({\mathbb{P}}^2\) (Q1568963)
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scientific article; zbMATH DE number 1463791
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Attracting basins in \({\mathbb{P}}^2\) |
scientific article; zbMATH DE number 1463791 |
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Attracting basins in \({\mathbb{P}}^2\) (English)
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22 June 2000
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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.
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holomorphic dynamics
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projective space
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attracting basins
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periodic fixed point
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homoclinic tangency
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