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Exploring universality in 1-D systems

Grant number: 19/16278-4
Support type:Regular Research Grants
Duration: December 01, 2019 - November 30, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Cooperation agreement: Imperial College, UK
Mobility Program: SPRINT - Projetos de pesquisa - Mobilidade
Principal Investigator:Edson de Faria
Grantee:Edson de Faria
Principal investigator abroad: Sebastian van Strien
Institution abroad: Imperial College London, England
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Assoc. 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)