Skip to main content

My mathematical expectations

Part of the Lecture Notes in Mathematics book series (LNM,volume 312)

Keywords

  • Ordinary Linear Differential Equation
  • Regular Singularity
  • Linear Differential System
  • Irregular Singular Point
  • Formal Series Solution

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H.L. Turrittin. "Asymptotic solutions of certain ordinary differential equations associated with multiple roots of the characteristic equations," Amer. Jour. of Math., 58 (1936) 364–376.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. _____, "Asymptotic distribution of zeros for certain exponential sums," Amer. Jour. of Math., 66 (1944) 199–228.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. H.L. Turrittin. "Stokes multipliers for asymptotic solutions of a certain differential equation," Trans, Amer. Math. Soc., 68 (1950) 304–329.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. _____ "Asymptotic expansions of solutions of ordinary linear differential equations containing a parameter," Annals of Math. Studies, vol. II, No. 29, Princeton: Princeton Univ. Press, (1952) 81–116.

    Google Scholar 

  5. _____ "Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point," Acta Mathematica, 93 (1955) 27–66.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. _____ "A peculiar solution of a modified Duffing's equation" (with W.J.A. Culmer), Ann Mat. Pura Appl. Ser. IV, 44 (1957) 23–33.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. _____ "Standardization and simplification of systems of linear differential equations involving a turning point" (with W.A. Harris, Jr.), SIAM J. Appl. Math 7 (1959) 316–324.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. _____ "Linear differential or difference equations with constant coefficients," Amer. Math. Monthly, 66 (1959) 869–875.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. _____ "The formal theory of systems of irregular homogeneous linear difference and differential equations," Boletin de la Sociedad Math. Mexicana, (1960) 255–264.

    Google Scholar 

  10. _____ "A canonical form for a system of linear difference equations," Ann. Mat. Pura Appl. Ser. IV, 58 (1962) 335–358.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. _____ "Reduction of ordinary differential equations to the Birkhoff canonical form," Trans. Amer. Math. Soc., 107 (1963) 485–507.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. _____ "Solvable related equations pertaining to turning point problems," Asymptotic solutions of differential equations and their applications, edited by Calvin H. Wilcox, John Wiley & Sons, (1964) 27–52.

    Google Scholar 

  13. H.L. Turrittin. "Stokes multipliers for the differential equation dny / dxn − y/x=0," Funkcialaj Ekvacioj, 6 (1964) 37–46.

    MathSciNet  Google Scholar 

  14. _____ "Convergent solutions of ordinary linear nonhomogeneous differential equations," Funkcialaj Ekvacioj, 12 (1969) 7–21.

    MathSciNet  MATH  Google Scholar 

  15. R.E. Langer. "The solution of the differential equation v‴+λzv′+3μλ2v=0 " Duke Math. J. 22 (1955) 525–542.

    CrossRef  MathSciNet  Google Scholar 

  16. _____ "On the asymptotic forms of ordinary linear differential equations of the third order in a region containing a turning point," Trans. Amer. Math. Math. Soc., 80 (1955) 93–123.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. _____ "The solutions of a class of ordinary linear differential equations of the third order in a region containing a multiple turning point," Duke Math. J. 23 (1956) 93–110.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. _____ "On the asymptotic solutions of a class of ordinary differential equations of the fourth order with a special reference to an equation of hydrodynamics," Trans. Amer. Math. Soc. 84 (1957) 144–191.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Y. Sibuya. "Simplification of a linear ordinary differential equation of the n-th order at a turning point," Arch. Rat. Mech. Anal., 13 (1963) 206–221.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. _____ "On the problem of turning points for a system of linear ordinary differential equations of higher orders," Proc. of Symposium Math. Res. Ctr., U.S. Army, Univ. Wisconsin, Madison, Wisc. (1964) 145–162, Wiley, N.Y. 1964.

    Google Scholar 

  21. W. Wasow. Asymptotic expansions for ordinary differential equations, Interscience Publishers, 1965, Chap. 8.

    Google Scholar 

  22. _____ "On turning point problems for systems with almost diagonal coefficient matrix," Funkcialaj Ekvacioj, 8 (1966) 143–170.

    MathSciNet  MATH  Google Scholar 

  23. _____ "The central connection problem at turning points of linear differential equations," Analytic theory of differential equation, Lecture notes in Mathematics, #183, Springer-Verlag, 1971, (Proc. of a conference at Western Mich. Univ.), 158–164.

    Google Scholar 

  24. L.A. MacColl. "On the distribution of the zeros of sums of exponentials of polynomials," Trans. Amer. Math. Soc., 36 (1934) 341–360.

    MathSciNet  MATH  Google Scholar 

  25. R.E. Langer. "The asymptotic location of the roots of a certain transcendental equation," Trans. Amer. Math. Soc., 31 (1929) 837–844.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. J.G. Van der Corput. "Rhythmische Systeme," Acta Math. 59 (1932) 209–328.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. J.B. McLeod. "On the distribution of eigenvalues of an n-th order equation," Quart, J. Math. Oxford (2), 17 (1966) 112–131.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. B.L.J. Braaksma. "Asymptotic analysis of a differential equation of Turrittin," SIAM J. Math. Anal, 2 (1971) 1–16.

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. H.L. Turrittin. "Stokes multipliers for the equation d3y/dx3 − y/x2=0," Lecture notes in mathematics, #183, Analytic theory of differential equations, (Proc. of Conf. at Western Mich. Univ. (1970) 145–157.

    Google Scholar 

  30. H. Scheffé. "Linear differential equations with two term recurrence formulas," J. Math. & Phys., 21 (1942) 240–249.

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. W. Loud & K.W. Blair. "Periodic solutions of x″ + cx′ + g(x)=Ef(t) under variation of certain parameters," SIAM J. Appl. Math. 8 (1960) 74–101.

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. W. Loud. "Periodic solutions of second order differential equations of Duffing type," Proc. U.S.-Japan Seminar, (1967) 199–224.

    Google Scholar 

  33. _____ "Branching phenomena for periodic solutions of nonautonomous piecewise linear systems," International Jour. of Nonlinear Mechanics, 5 (1969) 352–368.

    MathSciNet  MATH  Google Scholar 

  34. W.J.A. Culmer & W.A. Harris, Jr. "Convergent solutions of ordinary linear homogeneous difference equations," Pac. Jour. Math., 13 (1963) 1111–1138.

    CrossRef  MathSciNet  MATH  Google Scholar 

  35. W.A. Harris, Jr. & S. Tanaka. "On difference equations containing a parameter," Publ. of Research Inst. for Math. Sciences, Kyoto Univ., Ser. A, 2 (1966), 5–16.

    CrossRef  MathSciNet  MATH  Google Scholar 

  36. R. Gérard & A.H.M. Levelt. "Invariants mesurant l'irregularité en un point singulier des systemes d'équations différentielles linéariares," Notes published by the Institut de Recherche Mathématique Avancée de Strasbourg, 1972.

    Google Scholar 

  37. A.H.M. Levelt. "Formal theory of irregular singular points," (to appear), 1972.

    Google Scholar 

  38. H.L. Turrittin. "Reducing the rank of ordinary differential equations," Duke Math. Jour., 30 (1963) 271–274.

    CrossRef  MathSciNet  MATH  Google Scholar 

  39. D.A. Lutz. "On the reduction of rank of linear differential systems," U.S. Army Math. Research Center, Univ. of Wisc., Madison, Wisc., Report #1097, Aug., 1970, 1–18.

    Google Scholar 

  40. G.D. Birkhoff, "Equivalent singular points of ordinary linear differential equations," Math. Ann. 74 (1913), p. 136.

    MathSciNet  Google Scholar 

  41. W.B. Jurkat & D.A. Lutz. "Birkhoff reduction of two-dimensional linear differential systems at a singular point," U.S. Army Math. Research Center, Univ. of Wisc., Madison, Wisc., Report #1062, (1970), 1–33.

    Google Scholar 

  42. E.L. Ince. Ordinary Differential Equations, 1927 edition, p. 174.

    Google Scholar 

  43. K.O. Friedrichs. Special topics in analysis, New York Univ. Notes, 1953, page B-9.

    Google Scholar 

  44. L.M. Milne-Thompson. The calculus of finite differences, 1951, pp. 289–290.

    Google Scholar 

  45. W.A. Harris, Jr., Y. Sibuya & L Weinberg. "Holomorphic solutions of Linear differential systems at singular points," Arch. Rat. Mech. & Anal, 35 (1969), 245–248.

    CrossRef  MathSciNet  MATH  Google Scholar 

  46. F. Lettenmeyer. "Über die an einer Unbestimmtheitsstelle regulären Lösungen eines Systemes homogener linearen Differentialgleichunghen," S.-B. Bayer. Akad. Wiss. Munchen Math.-nat. Abt. (1926) 287–307.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1973 Springer-Verlag

About this paper

Cite this paper

Turrittin, H.L. (1973). My mathematical expectations. In: Harris, W.A., Sibuya, Y. (eds) Symposium on Ordinary Differential Equations. Lecture Notes in Mathematics, vol 312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060042

Download citation

  • DOI: https://doi.org/10.1007/BFb0060042

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06146-5

  • Online ISBN: 978-3-540-38353-6

  • eBook Packages: Springer Book Archive