Anosov dynamical systems

• Grant number: 13/02144-0
• Support Opportunities: Scholarships abroad - Research
• Start date: August 15, 2013
• End date: July 29, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Carlos Alberto Maquera Apaza
• Grantee: Carlos Alberto Maquera Apaza
• Host Investigator: Thierry Barbot
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Université d'Avignon et des Pays de Vaucluse, France

Abstract

The research project is devoted to study of "Anosov actions" and the related topic of "Anosov representation". This proposal is a pure fundamental research project involving several fields of mathematics concerning the notion of Anosov systems. Anosov systems is a central notion in dynamical systems, as perfect paradigms of structural stability. They also appear in a very natural and important way in several traditional fields of mathematics (number theory, Lie algebras, geometry,...). The objectives of this research project would last 2 years divided in essentially two tasks: I.- Topological aspects of Anosov systems;II.- Anosov representations in SL(n,IR). The topological classification of Anosov actions of IR^k is a long term program initied by C. Maquera and T. Barbot, until today, has been obtained fundamental results which will be important to continue this study. In direction of item (I), we intend to continue this study. On the other hand, the study of Anosov representations have been recently developed by the work of Labourie, Guichard, Wienhardt and Barbot as a tool to study the topology of representations of (Gromov) hyperbolic groups into Lie groups, and the related geometric structures as well. (AU)