Smooth pertubations of Lorenz-like flows

Author(s)

José Humberto Bravo Vidarte

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2014-04-04

Examining board members

Daniel Smania Brandão; Vítor Domingos Martins de Araújo; Alexander Eduardo Arbieto Mendoza; Maria José Pacífico

• Advisor: Daniel Smania Brandão

Abstract

Given a Geometric Lorenz Flow X on \'R POT. n+2\' of class \'C POT. k+1\'; by definition there exists a Poincaré map \'P IND. X\' of class \'C POT. k+1\'; often so-called Lorenz-type map [ABS83]. The main purpose in this dissertation is to show that under certain conditions the Lorenz-type map \'P IND.X\' can be associate to it a one-dimensional transformation \'f IND. X\' of class \'C POT. k\' (defined on an interval). This association is so-called the reduction transformation R; so we have \'RP IND. X\' = \'f IND. X\'. This association would allow us to study the dynamical properties for the original flow using techniques of one-dimensional dynamics of class \'C POT. k\' (AU)

• FAPESP's process: 09/17153-9 - Perturbations o Lorenz-like flows.
• Grantee: Jose Humberto Bravo Vidarte
• Support Opportunities: Scholarships in Brazil - Doctorate