On Halphen and Laguerre-Forsyth canonical forms of linear differential equations

František Neuman

Archivum Mathematicum (1990)

  • Volume: 026, Issue: 2-3, page 147-154
  • ISSN: 0044-8753

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Neuman, František. "On Halphen and Laguerre-Forsyth canonical forms of linear differential equations." Archivum Mathematicum 026.2-3 (1990): 147-154. <http://eudml.org/doc/18296>.

@article{Neuman1990,
author = {Neuman, František},
journal = {Archivum Mathematicum},
keywords = {linear differential equation; global transformation; Laguerre-Forsyth canonical form},
language = {eng},
number = {2-3},
pages = {147-154},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On Halphen and Laguerre-Forsyth canonical forms of linear differential equations},
url = {http://eudml.org/doc/18296},
volume = {026},
year = {1990},
}

TY - JOUR
AU - Neuman, František
TI - On Halphen and Laguerre-Forsyth canonical forms of linear differential equations
JO - Archivum Mathematicum
PY - 1990
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 026
IS - 2-3
SP - 147
EP - 154
LA - eng
KW - linear differential equation; global transformation; Laguerre-Forsyth canonical form
UR - http://eudml.org/doc/18296
ER -

References

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  1. J. M. Berkovich, Canonical forms of ordinary linear differential equations, Arch. Math. (Brno) 24 (1988), 25-42. (1988) Zbl0672.34005MR0983005
  2. G. D. Birkhoff, On the solutions of ordinary linear homogeneous differential equations of the third order, Ann. of Math. 12 (1910/11), 103-123. (1910) 
  3. O. Borůvka, Lineare Differentialtransformationen 2. Ordnung, VEB, Berlin 1967; English edition: Linear Differential Transformations of the Second Order, The English Univ. Press, London 1971. (1967) MR0463539
  4. M. Čadek, Form of general pointwise transformations of linear differential equations, Czechoslovak Math. J. 35 (110) (1985), 617-624. (1985) MR0809044
  5. A. R. Forsyth, Invariants, covariants and quotient-derivatives associated with linear differential equations, Philos. Trans. Roy. Soc. London Ser. A, 179 (1899), 377-489. 
  6. G. H. Halphen, Mémoire sur la réduction des équations différentielles linéaires aux formes intégrables, Mémoires presented par divers savants á l'Académie des sciences de l'Institut de France 28 (1884), 1-307. 
  7. Z. Hustý, Die Iteration homogener linearer Differentialgleichungen, Publ. Fac. Sci. Univ. J. E. Purkyně (Brno) 449 (1964), 23-56. (1964) MR0196166
  8. E. Laguerre, Sur les équations différentielles linéaires du troisième ordre, C. R. Acad. Sci. Paris 88 (1879), 116-118. 
  9. F. Neuman, Geometrical approach to linear differential equations of the n-th order, Rend. Mat. 5 (1972), 579-602. (Abstract: Some results on geometrical approach to linear differential equations of the n-th order. Comment. Math. Univ. Carolin. 12 (1971), 307-315). (1972) Zbl0257.34029MR0288337
  10. F. Neuman, Global canonical forms of linear differential equations, Math. Slovaca 33 (1983), 389-394. (1983) MR0720509
  11. F. Neuman, Criterion of global equivalence of linear differential equations, Proc. Roy. Soc. Edinburgh Sect. A 97 (1984), 217-221. (1984) Zbl0552.34009MR0751194
  12. F. Neuman, Global theory of ordinary linear homogeneous differential equations in the real domain, I and II, Aequationes Math. 33 and 34 (1987), 123-149 and 1-22. (1987) Zbl0676.34007MR0915867
  13. P. Stäckel, Über Transformationen von Differentialgleichungen, J. Reine Angew. Math. 111 (1893), 290-302. 
  14. E. J. Wilczynski, Projective differential geometry of curves and ruled surfaces, Teubner, Leipzig, 1906. (1906) 

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