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Spectral sequences for Morse-Bott and Morse-Novikov flows study

Grant number: 14/11943-6
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): September 01, 2014
Effective date (End): March 31, 2018
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher: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:12/18780-0 - Geometry of control systems, dynamical and stochastics systems, AP.TEM
Associated scholarship(s):15/10930-0 - Symplectic dynamics and spectral sequences, BE.EP.PD

Abstract

In this project , we propose to develop Conley's theory in the context of Morse-Bott and Morse-Novikov flows, associated to Morse-Bott and Morse circular functions, respectively. More specifically, we intend to use the algebraic theory of spectral sequences together with connection matrices to study continuation properties of these flows. We want to associate the topology of the manifold to the trajectories connecting critical manifolds (singularities, respectively) of a Morse-Bott flow (Morse-Novikov flow, respectively). We will consider a Morse-Bott chain complex (Novikov chain complex, respectively) such that its differential contains information on these trajectories. We will study the connection matrices and transition matrices obtained by the sweeping method adapted to this situation, in order to understand dynamical behaviors associated with each stage of the process. The ultimate goal is to understand the bifurcations that can occur in the steps associated to transition matrices when a one-parameter family of flows is considered.

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Scientific publications (4)
(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)
LIMA, D. V. S.; MANZOLI NETO, O.; DE REZENDE, K. A.. On handle theory for Morse-Bott critical manifolds. Geometriae Dedicata, v. 202, n. 1, p. 265-309, . (12/18780-0, 16/24707-4, 14/11943-6)
LIMA, DAHISY V. DE S.; MANZOLI NETO, OZIRIDE; DE REZENDE, KETTY A.; DA SILVEIRA, MARIANA R.. CANCELLATIONS FOR CIRCLE-VALUED MORSE FUNCTIONS VIA SPECTRAL SEQUENCES. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 51, n. 1, p. 259-311, . (15/10930-0, 12/18780-0, 14/11943-6)
LIMA, D. V. S.; RAMINELLI, S. A.; DE REZENDE, K. A.. HOMOTOPICAL CANCELLATION THEORY FOR GUTIERREZ-SOTOMAYOR SINGULAR FLOWS. JOURNAL OF SINGULARITIES, v. 23, p. 33-91, . (14/11943-6, 18/13481-0, 15/10930-0, 16/24707-4)
BERTOLIM, MARIA A.; LIMA, DAHISY V. S.; MELLO, MARGARIDA P.; DE REZENDE, KETTY A.; DA SILVEIRA, MARIANA R.. Algebraic and dynamical cancellations associated to spectral sequence. EUROPEAN JOURNAL OF MATHEMATICS, v. 3, n. 2, p. 387-428, . (12/18780-0, 14/11943-6)

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