Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917600259211264 |
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| author | Azuaje, R. |
| author_facet | Azuaje, R. |
| contents | In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamiltonian systems on cosymplectic and cocontact manifolds. We show that having a solvable Lie algebra of constants of motion for a Hamiltonian system is equivalent to having a solvable Lie algebra of symmetries of the vector field defining the dynamics of the system, which allows us to find the solutions of the equations of motion by quadratures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02218 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems Azuaje, R. Mathematical Physics In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamiltonian systems on cosymplectic and cocontact manifolds. We show that having a solvable Lie algebra of constants of motion for a Hamiltonian system is equivalent to having a solvable Lie algebra of symmetries of the vector field defining the dynamics of the system, which allows us to find the solutions of the equations of motion by quadratures. |
| title | Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2302.02218 |