Symmetries of functions on networks and of mappings on Minkowski spaces

• Grant number: 13/11108-7
• Support Opportunities: Scholarships abroad - Research
• Start date: January 01, 2014
• End date: December 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Míriam Garcia Manoel
• Grantee: Míriam Garcia Manoel
• Host Investigator: Richard Mark Roberts
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: University of Surrey, England

Abstract

The theory of dynamical systems which are equivariant with respect to group actions uses a number of fundamental tools from algebra and topology: group representation theory, invariant theory, normal forms, and singularity and bifurcation theory. Different `flavours' of these are needed to investigate in several directions as, for example, gradient, time-reversible, Hamiltonian and Poisson systems on Euclidean spaces. This project proposes two distinct directions. Using these tools, one aim is to investigate the class of gradient systems related to networks of coupled dynamical systems. In the second direction we propose a systematic study of equivariant systems defined on Minkowski spaces. This project will hold at the Department of Mathematics, Surrey University, Inglaterra under the supervision of professor Mark Roberts. This project also relates the project of a PhD student under my supervision. We expect that the results shall be of interest for researchers working on symmetries in a variety of contexts. (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)

MANOEL, MIRIAM; ROBERTS, MARK. Gradient systems on coupled cell networks. Nonlinearity, v. 28, n. 10, p. 3487-3509, OCT 2015. (13/11108-7)