6533b7d0fe1ef96bd125b7dc

RESEARCH PRODUCT

Darboux integrable system with a triple point and pseudo-abelian integrals

Aymen Braghtha

subject

0209 industrial biotechnologyPure mathematicsControl and OptimizationIntegrable systemTriple pointAbelian integrals[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]Darboux integrability[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)02 engineering and technologyType (model theory)01 natural sciencesIntegrating factor020901 industrial engineering & automationFOS: MathematicsLimit Cycle0101 mathematicsAbelian groupMathematics - Dynamical Systems34C07 34C08MathematicsNumerical AnalysisAlgebra and Number Theory010102 general mathematicsMathematical analysisLimit cyclesMathematics Subject ClassificationControl and Systems EngineeringBounded functionFoliation (geology)

description

We study pseudo-abelian integrals associated with polynomial perturbations of Dar-boux integrable system with a triple point. Under some assumptions we prove the local boundedness of the number of their zeros. Assuming that this is the only non-genericity, we prove that the number of zeros of the corresponding pseudo-abelian integrals is bounded uniformly for nearby Darboux integrable foliations.

yearjournalcountryeditionlanguage
2016-10-31
https://hal.archives-ouvertes.fr/hal-01388054v3/file/triplecase.pdf