On the nonexistence of rational first integrals for systems of linear differential equations

DOI10.1016/0024-3795(94)00122-7zbMath0843.34013OpenAlexW2048475542MaRDI QIDQ1911923

Andrzej Nowicki

Publication date: 28 April 1996

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(94)00122-7

zbMATH Keywords

linear differential equationsrational first integral

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Linear ordinary differential equations and systems (34A30) Differential algebra (12H05)

Related Items (18)

Polynomial Graded Subalgebras of Polynomial Algebras ⋮ Algebraic integrability of nilpotent planar vector fields ⋮ Rational constants of monomial derivations ⋮ On the nonexistence of rational first integrals for nonlinear systems and semiquasihomogeneous systems ⋮ Rational equivalence for enveloping algebras of three-dimensional Lie algebras ⋮ On generalized cyclotomic derivations ⋮ About algebraic integrability and non-integrability of ordinary differential equations ⋮ Rings of constants of linear derivations on Fermat rings ⋮ Painlevé analysis and normal forms theory ⋮ Families of \(k\)-derivations on \(k\)-algebras ⋮ Formal first integrals for periodic systems ⋮ \(n-1\) independent first integrals for linear differential systems in \(\mathbb{R}^n\) or \(\mathbb{C}^n\) ⋮ Finiteness of integrable \(n\)-dimensional homogeneous polynomial potentials ⋮ Constants and Darboux Polynomials for Tensor Products of Polynomial Algebras with Derivations ⋮ Monomial Derivations ⋮ Nonexistence of formal first integrals for general nonlinear systems under resonance ⋮ Nonexistence of formal first integrals for nonlinear systems under the case of resonance ⋮ Algebras of constants for some extensions of derivations

Cites Work

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• Rings of constants for \(k\)-derivations in \(k[x_ 1,\dots ,x_ n\)]
• A note on locally nilpotent derivations
• Rings and fields of constants for derivations in characteristic zero
• Locally nilpotent derivations and their applications. III
• On the nonexistence of constants of derivations: the proof of a theorem of Jouanolou and its development

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