Geodesic
Canonical forms of ordinary linear differential equations
Archivum mathematicum, Tome 24 (1988) no. 1, pp. 25-42 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 34A05, 34C20 
@article{ARM_1988_24_1_a3,
     author = {Berkovich, L. M.},
     title = {Canonical forms of ordinary linear differential equations},
     journal = {Archivum mathematicum},
     pages = {25--42},
     year = {1988},
     volume = {24},
     number = {1},
     mrnumber = {983005},
     zbl = {0672.34005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1988_24_1_a3/}
}
TY  - JOUR
AU  - Berkovich, L. M.
TI  - Canonical forms of ordinary linear differential equations
JO  - Archivum mathematicum
PY  - 1988
SP  - 25
EP  - 42
VL  - 24
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ARM_1988_24_1_a3/
LA  - en
ID  - ARM_1988_24_1_a3
ER  - 
%0 Journal Article
%A Berkovich, L. M.
%T Canonical forms of ordinary linear differential equations
%J Archivum mathematicum
%D 1988
%P 25-42
%V 24
%N 1
%U http://geodesic.mathdoc.fr/item/ARM_1988_24_1_a3/
%G en
%F ARM_1988_24_1_a3
Berkovich, L. M. Canonical forms of ordinary linear differential equations. Archivum mathematicum, Tome 24 (1988) no. 1, pp. 25-42. http://geodesic.mathdoc.fr/item/ARM_1988_24_1_a3/

[1] Л. M. Бepкoвич: O фaкmopuзaцuu oбыкнoвeнныx лuнeйныx дuффepeнцuaлъныx onepamopoв, npeoбpvзyeмыx в onepamopы c nocmoяннымu кoэффuцeнmaмu. Извecтия вyзoв. Maт. (Kaзaнcкий yнивepcитeт), I чacть, 4 (1965), 8-16; II чacть, 12 (167), 3-14.

[2] Л. M. Бepкoвич: O фaкmopuзaцuu u npuвoдuмocmu oбыкнoвeныx лuнeйныx дuффepeнцuaлъныx ypaвнeнuй 2-гo nopядкa. Tpyды 2-й Pecпyбл. кoнфep. мaтeмaтикoв Бeлopycии. Mинcк (Бeлopyc. yнивepcитeт), 1969, 165-170.

[3] L. M. Berkovich: Sur une classe d'équations différentielles nonautonomous et non-linéaires d'ordre n. Aгch. Math. (Brno) 6 (1970), 7-13.

[4] Л. M. Бepкoвич: Пpeoбpaзoвaнue oбыкнoвeнныx лuнeйныx дuффepeнцuaлъныx ypaвнeнuй. Kyйбышeвcкий yнивepcитeт. Kyйбышeв, 1978.

[5] Л. M. Бepкoвич : O npeoбpaзoвaнuu дuффepeнцuaлъныx ypaвнeнuй muna Шmypмa-Лuyвuлля. Фyнкц. Aнaлиз (Mocквa) 16 (1982), 42-44.

[6] Л. M. Бepкoвич : Зaдaчa Aлъфaнa oб эквuвaлeнmнocmu oбыкнoвeнныx лuнeйныx дuффepeнцuaлъныx ypaвнeнuй. Уcпexи мaт. нayк, 41 (1986), 183-184. | MR

[7] Л. M. Бepкoвич B. Г. Биpyлик: Дuффepeнцuaлъный pcзyлъmaнm u нeкomopыe eгo npuмeнeнuя. Диффepeнц. Уpaвн. (Mинcк), 22 (1986), 750-757. | MR

[8] P. Bohl: Darstellung und Anwendung der Invarianten der linearen Differentialgleichungen. Dorpat 1886 (manuscript), Russian edition: П. Бoль, Coбpaниe тpyдoв, Зинaтнe, Pигa, 1974, 8-35.

[9] O. Borůvka: Lineare Differentialtransformationen 2. Oгdnung. VEB, Berlin 1967, English edition: Linear Differential Transformations of the Second Order, The English Univ. Press, London 1971.

[10] O. Borůvka: Theory of the global properties of ordinary linear differential equations of the second order. Диффepeнц. Уpaвн. (Mинcк), 12, (1976), 1347-1383. | MR

[11] O. Boгůvka: Sur les sous-groupes planaires des groupes des dispersions des équations différentielles linéaires du deuxième ordre. Proc. Roy. Soc. Edinburg 97A (1984), 35-41. | MR

[12] F. Bгioschi: Sur les équations différentielles linéaires. Bulletin de la Soc. math. de Fгance, 7 (1879), 105-108.

[13] A. R. Foгsyth: Invariants, covariants and quotient-derivatives associated with linear differential equations. Philosophical Tгans. Roy. Soc. London 179A (1899), 377-489.

[14] G. Fгobenius: Über den Begriff der Irreductibilität der Theorie der linearen Differentialgleichungen. J. Reine Angew. Math. 76 (1873), 236-270.

[15] M. Greguš: Linearna diferencialna rovnica tretieho radu. Slov. Akad. vied. Bratislava 1981. | MR

[16] G.-H. Halphen: Mémoire sur la réduction des équations différentielles linéaires aux formes intégrables. In: Mémoires pгésentés paг divers savants a l'académie des sciences de l'institute de Fгance 28 (1884), 1-301.

[17] G.-H. Halphen: Sur les invariants des équations differentielles linéaires du quatrième ordre. Acta Math. 3 (1883/1884), 325-380. | MR

[18] Z. Hustý: Die Iteration homogener linearer Differentialgleichungen. Publ. Fac. Sci. Univ. J. E. Purkyně (Bгno), 449 (1964), 23-56. | MR

[19] L. Koenigsbeгger: Allgemeine Untersuchungen aus der Theorie der Differentialgleichungen. Leipzig, 1882.

[20] E. Laguerre: Sur les équations différentielles linéaires du troisième ordre. Comptes Rendus de l'Acad. des sci. Paris, 88 (1879), 116-118.

[21] G. Mammana: Decomposizione delle expressioni differenziali lineari omogenee improdotti di fattori simbolici e applicazione relativa allo studio delle equazione differenziali lineari. Math. Zeit. 33 (1931), 186-231. | MR

[22] F. Neuman: Criterion of global equivalence of linear differential equations of the n-th order. Proc. Roy. Soc. Edinburg, 97 A (1984), 217-221. | MR

[23] F. Neuman: Stationary groups of linear differential equations. Czechoslovak Math. J. 34 (1984), 645-663. | MR | Zbl

[24] O. Ore: Formale Theorie der linearen Differentialgleichungen. Journ. für die reine und angew. Math. 167 (1932), 221-234. | Zbl

[25] T. Peyovitch: Sur les semi-invariants des équations différentiates. Bulletin de la Societé Math. de France, 53 (1925), 208-225. | MR

[26] V. Šeda: On a class of linear differential equations of order n, $n \geq 3$. Časopis Pěst. Mat. 92 (1967), 247-259. | MR

[27] V. Šeda: Über die transformation der Differentialgleichungen n-ter Ordnung I + II. Časopis Pěst. Mat. 90 (1965), 385-412 + 92 (1967), 418-435.

[28] J. Suchomel: Пpeo6paзoвaнue лuнeйныx oднopoдныx дuффepeнцuaлъныx ypaвнeнuй выcшeгo nopядкa. Arch. Math. (Brno) 13 (1977), 41-45.

[29] E. J. Wilczynski: Projective Differential Geometry of Curves and Ruled Surfaces. Teubner, Leipzig, 1906.