Transition Matrices associated with the Morse-Witten Complex

• Grant number: 10/08579-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: September 01, 2010
• End date: 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
• Host 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

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

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. (12/18780-0, 10/08579-0)

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. (10/08579-0, 12/18780-0)

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, p. 44-pg., 2016-09-01. (10/08579-0, 12/18780-0)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

LIMA, Dahisy Valadão de Souza. Sequências espectrais dinâmicas para complexos de Morse-Novikov e Morse-Bott. 2014. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.