A counterexample to the “composition conjecture"

DOI10.1090/S0002-9939-02-06755-2zbMath1008.34024arXivmath/0201068OpenAlexW1957438355WikidataQ122923913 ScholiaQ122923913MaRDI QIDQ4547052

Fedor Pakovitch

Publication date: 20 August 2002

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

Full work available at URL: https://arxiv.org/abs/math/0201068

zbMATH Keywords

compositionspolynomialsfunctional equationsPoincaré center-focus problempolynomial Abel equation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Related Items (16)

Infinitesimal center problem on zero cycles and the composition conjecture ⋮ The center problem and composition condition for Abel differential equations ⋮ On polynomials orthogonal to all powers of a Chebyshev polynomial on a segment ⋮ An explicit bound of the number of vanishing double moments forcing composition ⋮ The monodromy problem and the tangential center problem ⋮ Centers for trigonometric Abel equations ⋮ On the center problem for generalized Abel equations ⋮ A partial positive answer to a Lijun-Yun conjecture ⋮ Parametric centers for trigonometric Abel equations ⋮ Generalized ‘second Ritt theorem’ and explicit solution of the polynomial moment problem ⋮ Cauchy-type integrals of algebraic functions ⋮ Solution of the parametric center problem for the Abel differential equation ⋮ Center conditions at infinity for Abel differential equations ⋮ Algebraic geometry of the center-focus problem for Abel differential equations ⋮ The composition conjecture for Abel equation ⋮ On polynomials orthogonal to all powers of a given polynomial on a segment

Cites Work

• Center conditions. II: Parametric and model center problems
• Center conditions. III: Parametric and model center problems
• Center conditions, compositions of polynomials and moments on algebraic curves
• Abel Equations: Composition Conjectures and the Model Problem
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