Il Nuovo Cimento B (1971-1996)

, Volume 106, Issue 9, pp 1059–1061 | Cite as

A note on integrability and chaos of reduced self-dual Yang-Mills equations and Yang-Mills equations

  • W. H. Steeb
  • N. Euler
  • P. Mulser
Note Brevi


From Yang-Mills equations in four dimensions we can derive ordinary differential equations with chaotic behaviour. On the other hand, we can find competely integrable ordinary differential equations from self-dual Yang-Mills equations in four dimensions. We describe a connection between these integrable and chaotic systems.


PACS 03.70 Theory of quantized fields 


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  1. [1]
    R. S. Ward:Commun. Math. Phys.,80, 563 (1981).ADSCrossRefGoogle Scholar
  2. [2]
    R. S. Ward:Gen. Relativ. Grav.,15, 105 (1983).ADSCrossRefGoogle Scholar
  3. [3]
    R. S. Ward:Nucl. Phys. B,236, 381 (1984).ADSCrossRefGoogle Scholar
  4. [4]
    R. S. Ward:Phys. Lett. A,102, 279 (1984).MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    R. S. Ward:Nonlinearity,1, 671 (1988).MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    L. J. Mason andG. A. J. Sparling:Phys. Lett. A,137, 29 (1989).MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    W.-H. Steeb:Problems in Mathematical Physics, Vol. II:Advanced Problems (Bibliographisches Institut, Mannheim, 1990).Google Scholar
  8. [8]
    W.-H. Steeb:A Handbook of Terms Used in Chaos and Quantum Chaos (Bibliographisches Institut, Mannheim, 1991).Google Scholar
  9. [9]
    W.-H. Steeb andN. Euler:Nonlinear Evolution Equations and Painlevé Test (World Scientific, Singapore, 1988).CrossRefGoogle Scholar
  10. [10]
    W.-H. Steeb, J. A. Louw andC. M. Villet:Phys. Rev. D,33, 1174 (1986).MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    P. Dahlqvist andG. Russberg:Phys. Rev. Lett.,65, 2837 (1990).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1991

Authors and Affiliations

  • W. H. Steeb
    • 1
  • N. Euler
    • 1
  • P. Mulser
    • 2
  1. 1.Department of Applied Mathematics and Nonlinear StudiesRand Afrikaans UniversityJohannesburgSouth Africa
  2. 2.Institut für Angewandte PhysikTechnische Hochschule DarmstadtDarmstadtDeutschland

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