On Lie’s problem and differential invariants of ODEs y″ = F(x, y)

Bibikov, P. V.

doi:10.1007/s10688-017-0191-2

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A Panorama Of Examples1

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2019

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Cited by 3 publications

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“…. Differential invariants of this action were computed by P. Bibikov [4]. In particular, h k = 0 for k ≤ 3, h 4 = 2, and h k = k − 1 for k ≥ 5.…”

Section: 12mentioning

confidence: 99%

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Poincaré Function for Moduli of Differential-Geometric Structures

Kruglikov¹

2019

MMJ

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The Poincaré function is a compact form of counting moduli in local geometric problems. We discuss its property in relation to V. Arnold's conjecture, and derive this conjecture in the case when the pseudogroup acts algebraically and transitively on the base. Then we survey the known counting results for differential invariants and derive new formulae for several other classification problems in geometry and analysis.

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“…. Differential invariants of this action were computed by P. Bibikov [4]. In particular, h k = 0 for k ≤ 3, h 4 = 2, and h k = k − 1 for k ≥ 5.…”

Section: 12mentioning

confidence: 99%

“…The point transformation pseudogroup leaving the class invariant is (x, y) → (X(x), cX (x) 1/2 y + Y (x)), it naturally extends to the space J 0 = R 2 (x, y) × R(f ). Differential invariants of this action were computed by P. Bibikov [4]. In particular, h k = 0 for k ≤ 3, h 4 = 2, and h k = k − 1 for k ≥ 5.…”

Section: A Panorama Of Examplesmentioning

confidence: 99%