Formal First Integrals Along Solutions of Differential Systems I

被引：0

作者：

Aparicio-Monforte, Ainhoa ^{[1
]}

Barkatou, Moulay ^{[1
]}

Simon, Sergi ^{[1
]}

Weil, Jacques-Arthur ^{[1
]}

机构：

[1] Johannes Kepler Univ Linz, Symbol Computat Res Inst, A-4040 Linz, Austria

来源：

ISSAC 2011: PROCEEDINGS OF THE 36TH INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION | 2011年

关键词：

Computer Algebra; Integrability; First Integrals; Linear Differential Systems; Rational Solutions; Differential Galois; HAMILTONIAN-SYSTEMS; GALOIS-GROUPS; EQUATIONS; ALGORITHM;

D O I：

暂无

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider an analytic vector field (x) over dot = X (x) and study, via a variational approach, whether it may possess analytic first integrals. We assume one solution Gamma is known and we study the successive variational equations along Gamma. Constructions in [MRRS07] show that Taylor expansion coefficients of first integrals appear as rational solutions of the dual linearized variational equations. We show that they also satisfy linear "filter" conditions. Using this, we adapt the algorithms from [Bas99, vHW97] to design new ones optimized to this effect and demonstrate their use. Part of this work stems from the first author's Ph.D. thesis(1) [AM10].

引用

页码：19 / 26

页数：8

共 16 条

[1]

Aparicio-Monforte A., 2010, THESIS U LIMOGES

[2]

Aparicio-Monforte Ainhoa, 2009, ARXIV09123538V1

[3]

Aparicio-Monforte Ainhoa, 2011, CHARACTERIZATION RED

[4]

Aparicio-Monforte Ainhoa, 2010, REDUCTION M IN PRESS

[5]

AUDIN M, 2001, COURS SPECIALISES, V8

[6] An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system [J].

Barkatou M.A. .

Applicable Algebra in Engineering, Communication and Computing, 1997, 8 (1) :1-23

[7] On rational solutions of systems of linear differential equations [J].

Barkatou, MA .

JOURNAL OF SYMBOLIC COMPUTATION, 1999, 28 (4-5) :547-567

[8] On the Moser- and super-reduction algorithms of systems of linear differential equations and their complexity [J].

Barkatou, Moulay A. ;

Pfluegel, Eckhard .

JOURNAL OF SYMBOLIC COMPUTATION, 2009, 44 (08) :1017-1036

[9]

Fulton W., 1991, GRADUATE TEXTS MATH, V129

[10]

HILALI A, 1987, NUMER MATH, V50, P429, DOI 10.1007/BF01396663

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