Renormalization and rigidity in one-dimensional dynamics

• Grant number: 12/06614-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: July 01, 2012
• End date: January 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Edson de Faria
• Grantee: Pablo Andrés Guarino Quiñones
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project aims to study rigidity problems in one-dimensional dynamics. This kind of problems are typically related to the dynamical behavior of a suitable operator, the renormalization operator, defined via return maps in some subspace of the space of the dynamical systems considered. The understanding of the behavior of this renormalization operator allows one to conclude certain rigidity properties of the original dynamics. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DE FARIA, EDSON; GUARINO, PABLO. REAL BOUNDS AND LYAPUNOV EXPONENTS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 36, n. 4, p. 1957-1982, APR 2016. (12/06614-8)

GUARINO, PABLO; MARTENS, MARCO; DE MELO, WELINGTON. RIGIDITY OF CRITICAL CIRCLE MAPS. Duke Mathematical Journal, v. 167, n. 11, p. 2125-2188, AUG 15 2018. (12/06614-8)

GUARINO, PABLO; DE MELO, WELINGTON. Rigidity of smooth critical circle maps. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, v. 19, n. 6, p. 1729-1783, 2017. (12/06614-8)