Iterated Function Systems

• Grant number: 23/03329-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2023
• End date: December 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Kevin Felipe Kühl Oliveira
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

The study of random dynamical systems is extremely relevant for modeling and understanding several natural systems (climate dynamics and certain classes of dynamic programming problems, for example). This project aims to study random dynamical systems from the perspective of iterative function systems. To this end, the project is divided into four periods, beginning with the construction and study of the Barnsley-Hutchinson operator, progressing to the development of the Barnsley chaos game, followed by the study of the construction of Markov chains through function iteration and Breiman's ergodic theorem and, finally, an application of the studied topics through the analysis of the fractal image compression method.