Rigidity of dissipative Lorenz maps with criticality

• Grant number: 17/25955-4
• Support type: Scholarships abroad - Research
• Effective date (Start): August 01, 2018
• Effective date (End): January 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal researcher: Márcio Ricardo Alves Gouveia
• Grantee: Márcio Ricardo Alves Gouveia
• Host: Sebastian Van Strien
• Home 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
• Research place: 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)