We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.


On inhomogeneous linear automorphisms of simple hamiltonian systems

  • 28 Accesses


The present paper is concerned with the inhomogeneous linear automorphisms of simple Hamiltonian systems. The generating functions of these automorphisms are obtained for the systems which admit the scalar-preserving isometry groups of higher orders. The Lie algebras of the corresponding infinitesimal automorphisms are classified into two types, the kinematical and dynamical algebras. The structures of these algebras are made clear on the basis of the generating functions.


  1. [1]

    A. Pais,Dynamical symmetry in particle physics, Rev. Mod. Phys.,38 (1966), pp. 215–255.

  2. [2]

    M. Bander -C. Itzykson,Group theory and hydrogen atom I, II, Rev. Mod. Phys.,38 (1966), pp. 330–345, pp. 346–358.

  3. [3]

    N. Mukunda -L. O'Raifeartaigh -E. C. Sudarshan,Characteristic noninvariance groups of dynamical systems, Phys. Rev. Letters,15 (1965), pp. 1041–1044.

  4. [4]

    J. L. Synge -B. A. Griffith,Principles of mechanics, 3rd ed., McGraw-Hill, New York, 1959.

  5. [5]

    L. A. Pars,A treatie on analytical dynamics, Wiley, New York, 1968.

  6. [6]

    M. Ikeda -T. Fujitani,On linear first integrals of natural systems in classical mechanics, Math. Japon.,15 (1971), pp. 143–153.

  7. [7]

    M. Ikeda -M. Kimura,On quadratic first integrals of natural systems in classical mechanics, Math. Japon.,16 (1971), pp. 159–171.

  8. [8]

    M. Ikeda -Y. Nishino,On classical dynamical systems admitting the maximum number of linearly independent quadratic first integrals, Math. Japon.,17 (1972), pp. 69–78.

  9. [9]

    Y. Nishino,On quadratic first integrals in the « central potential » problem for the configuration space of constant curvature, Math. Japon.,17 (1972), pp. 59–67.

  10. [10]

    M. Ikeda -Y. Nishino,On quadratic first integrals of a particular natural system in classical mechanics, Hokkaido Math. Jour.,1 (1972), pp. 154–163.

  11. [11]

    S. Heskia -S. A. Sofrouniou,The unitary group U(m) as the symmetry group of curved phase space, Jour. Math. Phys.,12 (1971), pp. 2280–2286.

  12. [12]

    M. Ikeda -Y. Nishino,On groups of scalar-preserving isometries in Riemannian spaces, with application to dynamical systems, Tensor, N. S.,27 (1973), pp. 295–305.

  13. [13]

    L. P. Eisenhart,Continuous group of transformations, Princeton Univ. Press, Princeton, 1933.

  14. [14]

    K. Yano,On n-dimensional Riemannian spaces admitting a group of motions of order n(n−1)/2+1, Trans. Amer. Math. Soc.,74 (1953), pp. 260–279.

  15. [15]

    L. I. Schiff,Quantum mechanics, 3rd ed., McGraw-Hill, New York, 1968.

Download references

Author information

Additional information

Entrata in Redazione il 6 dicembre 1974.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ikeda, M., Iwai, T. On inhomogeneous linear automorphisms of simple hamiltonian systems. Annali di Matematica 107, 263–278 (1975). https://doi.org/10.1007/BF02416476

Download citation


  • Generate Function
  • Hamiltonian System
  • Isometry Group
  • Linear Automorphism
  • Dynamical Algebra