Effective Algorithm of Analysis of Integrability via the Ziglin’s Method

详细信息    查看全文

• 作者：Vladimir Salnikov
• 关键词：Integrability ; Numerical approach ; Complexified systems ; Monodromy group ; Ziglin’s method ; 37J30 ; 34M35
• 刊名：Journal of Dynamical and Control Systems
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：20
• 期：4
• 页码：465-474
• 全文大小：313 KB
• 参考文献：1. Salnikov V. On numerical approaches to the analysis of topology of the phase space for dynamical integrability. Chaos, Solitons Fractals 2013;57.
  2. Arnold VI, Kozlov VV, Neistadt AI. Mathematical aspects of classical and celestial mechanics, Moscow, VINITI; 1985.
  3. Ziglin SL. Fun Anal Appl. 1982;16-7.
  4. Kozlov VV. Symmetries, topology and resonances in Hamiltonian mechanics, Izhevsk; 1995.
  5. Audin M. Les systèmes hamiltoniens et leur integrabilité, Cours Specilisés, SMF et EDP Sciences; 2001.
  6. Yoshida H. Cel Mech. 1983;31:363.
  7. Morales-Ruiz JJ. Differential Galois theory and non-integrability of hamiltonian systems. Basel: Birkhausen; 1999.
  8. Morales-Ruiz JJ, Ramis J-P. Meth Appl Anal. 2001;8(1):33-5, 97-11.
  9. Shafarevich IR. Basic notions of algebra, INT, Contemporary problems of mathematics.
  10. Roekaerts D, Yoshida H. J Phys A: Math Gen. 1988;21:3547-557. CrossRef
  11. Maciejewski AJ, God?iewski K. Rep Math Phys. 1999;44:133-42. CrossRef
  12. Bardin BS, Maciejewski AJ. Transcendental cases in the stability problem of conical precession of a satellite in a circular orbit. Qual Theory Dyn Syst. 2013;12(1):207-16.
  
• 作者单位：Vladimir Salnikov (1)
  
  1. Laboratoire de Mathématiques de l’INSA de Rouen, Avenue de l’Université, 76801, Saint-étienne-du-Rouvray Cedex, France
  
• ISSN：1573-8698

文摘

In this paper, we continue the description of the possibilities to use numerical simulations for mathematically rigorous computer-assisted analysis of integrability of dynamical systems. We sketch some of the algebraic methods of studying the integrability and present a constructive algorithm issued from the Ziglin’s approach. We provide some examples of successful applications of the constructed algorithm to physical systems.