Constants of motion and degeneration in Hamiltonian systems
- 1 August 1973
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 14 (8) , 1106-1115
- https://doi.org/10.1063/1.1666445
Abstract
A rigorous formulation of the connection between nonergodicity (degeneration) of the motion of a Hamiltonian system and existence of global constants of motion (isolating integrals) is proposed. Necessary and sufficient conditions for the occurrence of a properly defined kind of complete degeneration are given. Finally, a wide‐spread opinion is criticized about the mutual implications between complete degeneration and separability of the Hamilton‐Jacobi equation in more than one coordinate systems.Keywords
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