Godbillon–Vey sequence and Françoise algorithm

Autor: Pavao Mardešić, Dmitry Novikov, Jessie Pontigo-Herrera, L. Ortiz-Bobadilla
Přispěvatelé: Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Weizmann Institute of Science [Rehovot, Israël], Instituto de Matematicas (UNAM), Universidad Nacional Autónoma de México (UNAM), Israel Science Foundation grant 1167/17, Papiit (Dgapa UNAM) IN106217, ECOS Nord-Conacyt 249542, Fordecyt 265667
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Bulletin des Sciences Mathématiques
Bulletin des Sciences Mathématiques, Elsevier, 2019, 153, pp.72-85. ⟨10.1016/j.bulsci.2019.02.001⟩
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2019.02.001⟩
Popis: We consider foliations given by deformations d F + ϵ ω of exact forms dF in C 2 in a neighborhood of a family of cycles γ ( t ) ⊂ F − 1 ( t ) . In 1996 Francoise gave an algorithm for calculating the first nonzero term of the displacement function Δ along γ of such deformations. This algorithm recalls the well-known Godbillon–Vey sequences discovered in 1971 for investigation of integrability of a form ω. In this paper, we establish the correspondence between the two approaches and translate some results by Casale relating types of integrability for finite Godbillon–Vey sequences to the Francoise algorithm settings.
Databáze: OpenAIRE
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