Center conditions: Pull-back of differential equations

DOI10.1090/tran/7660zbMath1419.14083arXiv1708.06043OpenAlexW2963066370MaRDI QIDQ5227981

Yadollah Zare

Publication date: 7 August 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.06043

zbMATH Keywords

holomorphic foliationsPicard-Lefschetz theorycenter singularity

Mathematics Subject Classification ID

Real algebraic sets (14P05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Singularities of holomorphic vector fields and foliations (32S65) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Related Items (3)

On the center-focus problem for the equation \(\frac{\mathrm{d}y}{\mathrm{d}x} + \Sigma_{i=1}^n a_i(x) y^i = 0\), \(0\leq x \leq 1\) where \(a_i\) are polynomials ⋮ Brieskorn module and center conditions: pull-back of differential equations in projective space ⋮ Orbitally symmetric systems with applications to planar centers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Higher order Poincaré-Pontryagin functions and iterated path integrals
• Petrov modules and zeros of abelian integrals
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Relative cohomology of polynomial mappings
• Center conditions: Rigidity of logarithmic differential equations.
• Intersection matrices for certain singularities
• Abelian integrals in holomorphic foliations.
• Irreducible components of the space of holomorphic foliations of degree two in \(\mathbb{C} P(n)\), \(n\geq 3\)
• Compact analytical varieties
• Commuting holonomies and rigidity of holomorphic foliations
• An explicit bound for the multiplicity of zeros of generic Abelian integrals
• Polynomial systems: a lower bound for the Hilbert numbers
• Successive derivatives of a first return map, application to the study of quadratic vector fields

This page was built for publication: Center conditions: Pull-back of differential equations