0000000000133256

AUTHOR

Aymen Braghtha

showing 2 related works from this author

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

2016

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.

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)
researchProduct

Darboux systems with a cusp point and pseudo-abelian integrals

2018

International audience; We study pseudo-abelian integrals associated with polynomial deformations of Darboux systems having a cuspidal singularity. Under some genericity hypothesis we provide locally uniform boundedness of on the number of their zeros.

[ MATH ] Mathematics [math]Cusp (singularity)Pure mathematicsPolynomialApplied Mathematics[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]010102 general mathematics[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Darboux integrability[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Pseudo-abelian integrals[MATH] Mathematics [math]01 natural sciences010101 applied mathematicsLimit cyclesSingularityUniform boundednessPoint (geometry)First integral0101 mathematicsAbelian groupMSC : 34C07 ; 34C08[MATH]Mathematics [math]AnalysisMathematics
researchProduct