Ergodic Theory of Normal Numbers

• Grant number: 25/04825-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2025
• End date: December 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Mateus Blanco de Sousa
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 23/13706-0 - EPSRC-FAPESP predicting critical transitions in complex dynamical networks: reduction and learning, AP.TEM

Abstract

This research project explores the connection between ergodic theory and normal numbers. A real number is normal in a given base if its digits exhibit uniform statistical behavior. Ergodic theory provides a powerful framework to study normality. In this project, we investigate classical results such as Weyl's criterion and examine how ergodicity of certain dynamical systems can be used to establish and construct normal numbers. We explore developments in the interplay between ergodic averages. (AU)