Exploring universality in 1-D systems

• Grant number: 19/16278-4
• Support Opportunities: Regular Research Grants
• Start date: December 01, 2019
• End date: November 30, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Agreement: Imperial College, UK
• Mobility Program: SPRINT - Projetos de pesquisa - Mobilidade
• Principal Investigator: Edson de Faria
• Grantee: Edson de Faria
• Principal researcher abroad: Sebastian van Strien
• Institution abroad: Imperial College London, England
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated researchers: Edson Vargas ; Trevor Clark
• Associated research grant: 16/25053-8 - Dynamics and geometry in low dimensions, AP.TEM

Abstract

The purpose of this work is to build on the recently developed cornerstones in one-dimensional dynamics, specifically complex bounds and quasi-symmetric rigidity for smooth maps, in order to extend the current renormalization technology to the setting of maps which are no longer required to be real analytic. More specifically, the purpose is to tackle the three research directions (A): non-analytic smooth systems with geometric scaling, (B): smooth systems with flat critical points with polynomial scaling, (C): systems with strong asymmetries with super-exponential scaling and non-universality. (AU)