Point equivalence of second-order ODEs: Maximal invariant classification order

被引：7

作者：

Milson, Robert ^{[1
]}

Valiquette, Francis ^{[2
]}

机构：

[1] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 3J5, Canada

[2] SUNY Coll New Paltz, Dept Math, New Paltz, NY 12561 USA

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2015年 / 67卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Differential invariants; Moving frames; Painleve equations; Point transformations; Second-order ordinary differential equations; DIFFERENTIAL-EQUATIONS; LINEARIZATION;

D O I：

10.1016/j.jsc.2014.08.003

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We show that the local equivalence problem of second-order ordinary differential equations under point transformations is completely characterized by differential invariants of order at most 10 and that this upper bound is sharp. We also demonstrate that, modulo Cartan duality and point transformations, the Painleve-I equation can be characterized as the simplest second-order ordinary differential equation belonging to the class of equations requiring 10th order jets for their classification. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：16 / 41

页数：26

共 50 条

[1] Necessary conditions of point equivalence of second-order ODEs to the fifth Painleve equation
Bagderina, Yu Yu
[J]. VII INTERNATIONAL CONFERENCE PROBLEMS OF MATHEMATICAL PHYSICS AND MATHEMATICAL MODELLING, 2019, 1205
[2] Necessary Conditions for Point Equivalence of Second-Order Odes to the Sixth Painlevé Equation
Bagderina Y.Y.
[J]. Journal of Mathematical Sciences, 2019, 242 (5) : 595 - 607
[3] EQUIVALENCE CLASSES OF THE SECOND ORDER ODEs WITH THE CONSTANT CARTAN INVARIANT
Kartak, Vera V.
[J]. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2011, 18 (04) : 613 - 640
[4] Equivalence Classes of the Second Order Odes with the Constant Cartan Invariant
Vera V. Kartak
[J]. Journal of Nonlinear Mathematical Physics, 2011, 18 : 613 - 640
[5] Equivalence problem for first-order and second-order ODEs with a quadratic restriction
Bayrakdar, Tuna
Turhan, Ayse
[J]. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2024,
[6] EQUIVALENCE OF SECOND-ORDER ODES TO EQUATIONS OF FIRST PAINLEVE EQUATION TYPE
Bagderina, Yu. Yu.
[J]. UFA MATHEMATICAL JOURNAL, 2015, 7 (01): : 19 - 30
[7] Point Classification of Second Order ODEs: Tresse Classification Revisited and Beyond
Kruglikov, Boris
[J]. DIFFERENTIAL EQUATIONS: GEOMETRY, SYMMETRIES AND INTEGRABILITY - THE ABEL SYMPOSIUM 2008, 2009, 5 : 199 - 221
[8] Abstraction Principles and the Classification of Second-Order Equivalence Relations
Ebels-Duggan, Sean C.
[J]. NOTRE DAME JOURNAL OF FORMAL LOGIC, 2019, 60 (01) : 77 - 117
[9] Integrating factors for second-order ODEs
Cheb-Terrab, ES
Roche, AD
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 1999, 27 (05) : 501 - 519
[10] Nonlinear systems of second-order ODEs
Cerda, Patricio
Ubilla, Pedro
[J]. BOUNDARY VALUE PROBLEMS, 2008, 2008 (1)

← 1 2 3 4 5 →