A brief history of Kovalevskaya exponents and modern developments

DOI10.1070/RD2000V005N01ABEH000120zbMath0947.37031OpenAlexW4256460671MaRDI QIDQ1577148

Alain Goriely

Publication date: 30 August 2000

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rd2000v005n01abeh000120

zbMATH Keywords

formal solutionintegrable equationintegrability theorymotion of a rigid bodyKovalevskaya exponents

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Nonlinear differential equations in abstract spaces (34G20) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25)

Related Items (10)

Singularity analysis in planar vector fields ⋮ Foliated affine and projective structures ⋮ Kovalevskaya exponents, weak Painlevé property and integrability for quasi-homogeneous differential systems ⋮ Quadratic differential equations in three variables without multivalued solutions. I ⋮ Lotka-Volterra equations in three dimensions satisfying the Kowalevski-Painlevé property ⋮ Painlevé analysis and normal forms theory ⋮ Differential Equations in Algebras ⋮ Global properties of Kovalevskaya exponents ⋮ On the multipliers at fixed points of quadratic self-maps of the projective plane with an invariant line ⋮ A survey on the Kovalevskaya exponents and their applications

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