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Transition matrices associated with the Morse-Witten complex

Grant number: 10/08579-0
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): September 01, 2010
Effective date (End): July 31, 2014
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Ketty Abaroa de Rezende
Grantee:Dahisy Valadão de Souza Lima
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:07/06896-5 - Geometry of control, dynamical and stochastic systems, AP.TEM

Abstract

In this project we will adopt a Morse-Witten approach via Conley index theory to associate the topology of the manifold to the trajectories connecting critical points of a gradient flow which define the moduli spaces. Some of these flow connections are registered in the integer entry connection matrix. We will study the connection and transition matrices which appear in the Sweeping Algorithm applied to this differential, the initial connection matrix, with the objective of better understanding the dynamical behaviour at each step. In particular, we would like to understand the bifurcations which occur in the transition matrix stages as well as investigate the effects on the compactified moduli spaces of higher dimensions.

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)
BERTOLIM, M. A.; LIMA, D. V. S.; MELLO, M. P.; DE REZENDE, K. A.; DA SILVEIRA, M. R. A global two-dimensional version of Smale's cancellation theorem via spectral sequences. Ergodic Theory and Dynamical Systems, v. 36, n. 6, p. 1795-1838, SEP 2016. Web of Science Citations: 2.
LIMA, DAHISY V. DE S.; DE REZENDE, KETTY A. CONNECTION MATRICES FOR MORSE-BOTT FLOWS. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 44, n. 2, p. 471-495, DEC 2014. Web of Science Citations: 0.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.