Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.19950 |
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Sommario:
- We study lifts of integrable systems by means of generalized Stäckel geometry. To this aim, we present the notion of Stäckel lift as a unified setting for the construction of new classes of integrable Hamiltonian systems of physical interest. The Stäckel lift extends the geometric framework underlying both the Riemannian and the Lorentzian-type classical Eisenhart lifts. Moreover, we prove that Hamiltonian systems constructed through momentum-dependent Stäckel matrices are naturally endowed with a non-trivial symplectic-Haantjes structure. We further illustrate applications to magnetic systems separable in cylindrical coordinates; we describe them within the Stäckel framework by means of modified Stäckel basis. We also show that explicitly momentum-dependent lifting matrices produce systems interpretable as gravitational waves, or momentum-dependent metrics of Hamilton and Finsler geometries, with potential applications in modified gravity theories.