350 rub
Journal Dynamics of Complex Systems - XXI century №3 for 2010 г.
Article in number:
On the Transcendental Functions Entered by Integration of the Differential Equations
Keywords: analytical theory of the differential equations integration in finite terms algebraic curves groups of the birational transformations elliptic functions abelian functions
Authors:
A.N. Bogolyubov, M.D. Malykh
Abstract:
Various approaches to integration of systems of nonlinear ordinary differential equations in finite terms are considered and how this concept can be introduced without fixing a class of transcendental functions introducing by integration is shown.
Pages: 35-38
References
  1. Хованский А.Г. Топологическая теория Галуа. М.: ЦНМО. 2008.
  2. Добровольский В.А., Стрельцын Ж., Локоть Н.В. Михаил Николаевич Лагутинский (1871-1915) // Историко-математические исследования. Вторая серия. Вып. 6 (41). M.: 2001.
  3. Cheb-Terrab E.S., Kolokolnikov T.Computer Algebra Solving of First Order ODEs // http: //www.cs.uwaterloo.ca/ ecterrab/publications.htmlComputer Physics Communications. 101. 1997.
  4. Painlevé P. Leçons sur la theorie analytique des equations
    differentielles. Paris, 1897 = Œuvres. V. 1. Paris. 1971
  5. Painlevé P.Приложениеккниге P. Boutroux // Œuvres. V. 2. Paris. 1974. P. 767 -813.
  6. Шафаревич И.Р. Основы алгебраической геометрии. Т. 1. М.: Наука. 1988
  7. Ritt J.F. Integration in finite terms, Liouville theory of elementary methods. N.-Y. 1948.
  8. Голубев В.В. Лекции по интегрированию уравнений движения тяжелого твердого тела. ГИТТЛ. 1953.
  9. Enriques F. Le superficie algebriche. Bologna. N. Zanichelli. 1949.