Dynamics of Asymptotically Holomorphic Mappings

• Grant number: 25/25637-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: January 01, 2026
• End date: August 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Edson de Faria
• Grantee: Pingao Sun
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 23/13706-0 - EPSRC-FAPESP predicting critical transitions in complex dynamical networks: reduction and learning, AP.TEM

Abstract

The aim of this project is to develop a systematic study of the dynamics of asymptotically holomorphic mappings acting on the Riemann sphere or the complex plane. Such transformations are important generalizations of rational transformations on the Riemann sphere, as well as transcendental transformations on the complex plane, or even polynomial-type transformations (à la Douady-Hubbard) which, however, still lack a general theory. (AU)