6533b862fe1ef96bd12c77a5
RESEARCH PRODUCT
Godbillon–Vey sequence and Françoise algorithm
Pavao MardešićDmitry NovikovJessie Pontigo-herreraL. Ortiz-bobadillasubject
SequenceFrançoise algorithmGeneral Mathematics010102 general mathematicsTerm (logic)IntegrabilityMelnikov functions01 natural sciencesMathematics::K-Theory and HomologyDisplacement functionMAP0101 mathematics[MATH]Mathematics [math]AlgorithmGodbillon–Vey sequenceMathematicsdescription
Abstract 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-07-01 |