Point transformations and linearizability of second-order ordinary differential equations

Gusyatnikova, V. N.; Yumaguzhin, V. A.

doi:10.1007/bf01137072

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Corollary 42 There Exists a Unique Horizontal Subspace H2

Isotropy Algebras1

Four Types Of Equations1

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1996

2021

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Cited by 9 publications

(11 citation statements)

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“…The following statement is well-known, see [4,7,9,15,[21][22][23]25], and [26]. From this proposition, we get (1).…”

Section: Isotropy Algebrasmentioning

confidence: 82%

Differential Invariants of Second Order ODEs, I

Yumaguzhin

2009

Acta Appl Math

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This paper is devoted to differential invariants of equations y = a 3 (x, y)y 3 + a 2 (x, y)y 2 + a 1 (x, y)y + a 0 (x, y).w.r.t. point transformations. The natural bundle of these equations and its bundles of kjets of sections, k = 0, 1, 2, . . . , are considered. The action of the pseudogroup of all point transformations on these bundles is investigated. Tensor differential invariants distinguishing orbits of this action on jet bundles of second and third orders are constructed. A complete collection of generators and their differential syzygies is obtained for the algebra of all scalar differential invariants of a wide class of considered equations containing generic equations.

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“…The following statement is well-known, see [4,7,9,15,[21][22][23]25], and [26]. From this proposition, we get (1).…”

Section: Isotropy Algebrasmentioning

confidence: 82%

Differential Invariants of Second Order ODEs, I

Yumaguzhin

2009

Acta Appl Math

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“…Four different types of equations (1) with conditions (6). Type Equation According to Theorem 1 any equation (1) of Type I can be transformed by point transformations (2) into the canonical form: (11) y ′′ = e y + t(x)y + s(x).…”

Section: Four Types Of Equationsmentioning

confidence: 99%

Equivalence Classes of the Second Order Odes with the Constant Cartan Invariant

Kartak

2021

JNMP

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“…This means that ω (2) is a unique obstruction to the linearizability of equations (1) by point transformations. Below, we give the independent proof of this fact.…”

Section: Corollary 42 There Exists a Unique Horizontal Subspace Hmentioning

confidence: 99%

“…Corollary 4.7. The form ω (2) is a unique obstruction to the linearizability of ODEs (1) by point transformations.…”

Section: Corollary 42 There Exists a Unique Horizontal Subspace Hmentioning

confidence: 99%