Rigidity of dissipative Lorenz maps with criticality

• Grant number: 17/25955-4
• Support Opportunities: Scholarships abroad - Research
• Start date: August 01, 2018
• End date: January 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Márcio Ricardo Alves Gouveia
• Grantee: Márcio Ricardo Alves Gouveia
• Host Investigator: Sebastian Van Strien
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Institution abroad: Imperial College London, England
• Associated research grant: 13/24541-0 - Ergodic and qualitative theory of dynamical systems, AP.TEM

Abstract

We are going to study the dynamics of maps acting on the interval, with a unique point of discontinuity, where the one-sided derivatives exists, and whose derivative is positive and strictly smaller than one everywhere. Such applications are called dissipative Lorenz maps. We will also assume that those Lorenz maps have criticality. More precisely we will be interested on the rigidity classes of these maps and on the regularity of the leaves from the lamination determined by that classes. (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)

CLARK, TREVOR; GOUVEIA, MARCIO. Hyperbolicity of renormalization for dissipative gap mappings. Ergodic Theory and Dynamical Systems, v. 42, n. 10, p. 42-pg., 2021-09-03. (17/25955-4, 13/24541-0)