CANCELLATIONS FOR CIRCLE-VALUED MORSE FUNCTIONS VIA SPECTRAL SEQUENCES

Autor(es)

Lima, Dahisy V. de S. ^[1] ; Manzoli Neto, Oziride ^[2] ; de Rezende, Ketty A. ^[1] ; da Silveira, Mariana R. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, IMECC, Campinas, SP - Brazil

^[2] Univ Sao Paulo, ICMC, Sao Carlos, SP - Brazil

^[3] Univ Fed ABC, CMCC, Santo Andre, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 51, n. 1, p. 259-311, MAR 2018.
• Citações Web of Science: 0

Resumo

A spectral sequence analysis of a filtered Novikov complex (N-{*}(f), Delta) over Z ((t)) is developed with the goal of obtaining results relating the algebraic and dynamical settings. Specifically, the unfolding of a spectral sequence of (N-{*}(f), Delta) and the cancellation of its modules is associated to a one parameter family of circle-valued Morse functions on a surface and the dynamical cancellations of its critical points. The data of a spectral sequence computed for (N-{*}(f), Delta) is encoded in a family of matrices Delta(r) produced by the Spectral Sequence Sweeping Algorithm (SSSA), which has as its initial input the differential Delta. As one ``turns the pages{''} of the spectral sequence, differentials which are isomorphisms produce cancellation of pairs of modules. Corresponding to these cancellations, a family of circle-valued Morse functions f(r) is obtained by successively removing the corresponding pairs of critical points of f. We also keep track of all dynamical information on the birth and death of connecting orbits between consecutive critical points, as well as periodic orbits that arise within a family of negative gradient flows associated to f(r). (AU)

• Processo FAPESP: 15/10930-0 - Dinâmica simplética e sequências espectrais
• Beneficiário: Dahisy Valadão de Souza Lima
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
• Processo FAPESP: 12/18780-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 14/11943-6 - Sequências espectrais no estudo de fluxos de Morse-Bott e Morse-Novikov
• Beneficiário: Dahisy Valadão de Souza Lima
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado