Loading [Contrib]/a11y/accessibility-menu.js
Published Online: 04 June 1998
Accepted: January 1996
Journal of Mathematical Physics 37, 1772 (1996); https://doi.org/10.1063/1.531496
more...View Affiliations
  • Dipartimento di Matematica, Università di Perugia, 06123 Perugia, Italy
It is shown that the complete symmetry group for the Kepler problem, as introduced by Krause, can be derived by Lie group analysis. The same result is true for any autonomous system.
  1. 1. J. Krause, J. Math. Phys. 35, 5734 (1994). Google ScholarScitation
  2. 2. W. F. Ames, Nonlinear Partial Differential Equations in Engineering, Vol. 2 (Academic, New York, 1972). , Google Scholar
  3. 3. G. W. Bluman and J. D. Cole, Similarity Methods for Differential Equations (Springer-Verlag, Berlin, 1974). Google Scholar
  4. 4. L. V. Ovsjannikov, Group Analysis of Differential Equations (Academic, New York, 1982). Google Scholar
  5. 5. P. J. Olver, Applications of Lie Groups to Differential Equations (Springer-Verlag, Berlin, 1986). Google Scholar
  6. 6. G. W. Bluman and S. Kumei, Symmetries and Differential Equations (Springer-Verlag, Berlin, 1989). Google Scholar
  7. 7. H. Stephani, Differential Equations. Their Solution Using Symmetries (Cambridge University, Cambridge, 1989). Google Scholar
  8. 8. J. M. Hill, Differential Equations and Group Methods for Scientists and Engineers (CRC, Boca Raton, FL 1992). Google Scholar
  9. 9. CRC Handbook of Lie Group Analysis of Differential Equations, Vol. I: Symmetries, Exact Solutions, and Conservation Laws, edited by N. H. Ibragimov (CRC, Boca Raton, FL, 1994). Google Scholar
  10. 10. M. Braun, Differential Equations and Their Applications (Springer-Verlag, Berlin, 1983). Google Scholar
  11. 11. CRC Handbook of Lie Group Analysis of Differential Equations, Vol. II: Applications in Engineering and Physical Sciences, edited by N. H. Ibragimov (CRC, Boca Raton, FL 1995). Google Scholar
  12. 12. M. C. Nucci, Interactive REDUCE programs for calculating Lie point, nonclassical, Lie-Bäcklund, and approximate symmetries of differential equations: manual and floppy disk, in CRC Handbook of Lie Group Analysis of Differential Equations. Vol. III: New Trends, edited by N. H. Ibragimov (CRC, Boca Raton, FL 1996), pp. 415–481. Google Scholar
  13. © 1996 American Institute of Physics.