Sayani Bera
IACS, Kolkata
August 7, 2025
Fatou-Bieberbach domains, stable manifolds and attracting basins.: Fatou-Bieberbach domains in $\mathbb{C}^k, \ k \ge 2$ are proper subdomains of $\mathbb{C}^k, \ k \ge 2$ that are biholomorphic to $\mathbb{C}^k, \ k \ge 2$. Such domains clearly do not exist in $\mathbb{C}$ and further, arise naturally from dynamics of automorphisms of $\mathbb{C}^k, \ k \ge 2$ as attracting basins of fixed points. The goal of this talk is to discuss the relevance of this observation in the context of stable manifolds (sets) arising from holomorphic dynamical systems on complex manifolds. Further, we will discuss a generalization of the stable manifold theorem (on complex manifolds), a question originally raised due to Bedford in 2000. This is a uniformisation problem, which connects with attracting basins of non-autonomous (holomorphic) dynamical models in $\mathbb{C}^k, \ k \ge 2$, and additionally produces more examples of Fatou-Bieberbach domains. This is a joint work with Kaushal Verma.
IACS, Kolkata
August 7, 2025
Fatou-Bieberbach domains, stable manifolds and attracting basins.: Fatou-Bieberbach domains in $\mathbb{C}^k, \ k \ge 2$ are proper subdomains of $\mathbb{C}^k, \ k \ge 2$ that are biholomorphic to $\mathbb{C}^k, \ k \ge 2$. Such domains clearly do not exist in $\mathbb{C}$ and further, arise naturally from dynamics of automorphisms of $\mathbb{C}^k, \ k \ge 2$ as attracting basins of fixed points. The goal of this talk is to discuss the relevance of this observation in the context of stable manifolds (sets) arising from holomorphic dynamical systems on complex manifolds. Further, we will discuss a generalization of the stable manifold theorem (on complex manifolds), a question originally raised due to Bedford in 2000. This is a uniformisation problem, which connects with attracting basins of non-autonomous (holomorphic) dynamical models in $\mathbb{C}^k, \ k \ge 2$, and additionally produces more examples of Fatou-Bieberbach domains. This is a joint work with Kaushal Verma.