Scaling symmetries and canonoid transformations in Hamiltonian systems
Abstract
In this paper, we investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case, we pay special attention to non-standard (non-canonical) symmetries, in particular scaling symmetries and canonoid transformations, as they provide new interesting tools for the qualitative study of these systems. Our main results are the characterizations of these non-standard symmetries and the analysis of their relation with conserved (or dissipated) quantities.
- Publication:
-
International Journal of Geometric Methods in Modern Physics
- Pub Date:
- March 2024
- DOI:
- 10.1142/S0219887824500774
- arXiv:
- arXiv:2306.15108
- Bibcode:
- 2024IJGMM..2150077A
- Keywords:
-
- Hamiltonian systems;
- generalized Noether’s theorem;
- scaling symmetries;
- cosymplectic geometry;
- contact geometry;
- Mathematical Physics
- E-Print:
- 22 pages. Comments are welcome