On classification problems in the theory of differential equations: Algebra + geometry

DOI10.2298/PIM1817033BzbMath1474.34252WikidataQ115229797 ScholiaQ115229797MaRDI QIDQ4985633

Alexander Malakhov, P. V. Bibikov

Publication date: 24 April 2021

Published in: Publications de l'Institut Math?matique (Belgrade) (Search for Journal in Brave)

zbMATH Keywords

differential equationsymmetry groupjet spacedifferential invariantalgebraic manifoldpolynomial dependence

Mathematics Subject Classification ID

Birational automorphisms, Cremona group and generalizations (14E07) Geometric methods in ordinary differential equations (34A26) Symmetries, invariants of ordinary differential equations (34C14)

Cites Work

• Solving local equivalence problems with the equivariant moving frame method
• Petrov invariants of Hamiltonian systems with a control parameter
• Projective classification of binary and ternary forms
• Global Lie-Tresse theorem
• Symmetries of second-order ordinary differential equations and Elie Cartan's method of equivalence
• Feedback differential invariants
• The local equivalence problem for \(d^ 2y/dx^ 2=F(x,y,dy/dx)\) and the Painlevé transcendents
• A differential geometric characterization of the first Painlevé transcendent
• Equivalence of holonomic differential equations
• Point equivalence of functions on the 1-jet space \(J^{1} \mathbb{R}\)
• Equivalence of second-order ordinary differential equations to Painlevé equations
• Point Classification of Second Order ODEs: Tresse Classification Revisited and Beyond
• Classification of Second-Order Ordinary Differential Equations Admitting Lie Groups of Fibre-Preserving Point Symmetries
• Group analysis of ordinary differential equations and the invariance principle in mathematical physics (for the 150th anniversary of Sophus Lie)
• Finite Subgroups of the Plane Cremona Group
• Lie algebras associated with scalar second-order ordinary differential equations
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