Attracting basins in \({\mathbb{P}}^2\)
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.
scientific article; zbMATH DE number 1463791