Conformal bi-Hamiltonian structure and integrability of an interacting Pais-Uhlenbeck oscillator
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915796855291904 |
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| author | Felski, Alexander Fring, Andreas |
| author_facet | Felski, Alexander Fring, Andreas |
| contents | We investigate an interacting Pais-Uhlenbeck oscillator with a Landau-Ginzburg type interaction term and analyse its classical dynamics from a geometric and numerical point of view. We show that the resulting fourth-order equation of motion admits a conformal bi-Hamiltonian formulation, possesses a non-trivial set of Lie symmetries and we demonstrate the existence of bounded and regular trajectories in representative parameter regimes. By establishing an explicit correspondence with an integrable generalised Hénon-Heiles system, we show that the interacting higher-derivative dynamics inherits the integrability properties of the latter. This connection allows us to construct a second conserved Hamiltonian, to clarify the geometric origin of separability, and to obtain explicit classical solutions in terms of elliptic functions. Our results provide a concrete example of an interacting higher-derivative system for which integrability and periodic classical solutions can be established in a fully explicit manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12858 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conformal bi-Hamiltonian structure and integrability of an interacting Pais-Uhlenbeck oscillator Felski, Alexander Fring, Andreas Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics We investigate an interacting Pais-Uhlenbeck oscillator with a Landau-Ginzburg type interaction term and analyse its classical dynamics from a geometric and numerical point of view. We show that the resulting fourth-order equation of motion admits a conformal bi-Hamiltonian formulation, possesses a non-trivial set of Lie symmetries and we demonstrate the existence of bounded and regular trajectories in representative parameter regimes. By establishing an explicit correspondence with an integrable generalised Hénon-Heiles system, we show that the interacting higher-derivative dynamics inherits the integrability properties of the latter. This connection allows us to construct a second conserved Hamiltonian, to clarify the geometric origin of separability, and to obtain explicit classical solutions in terms of elliptic functions. Our results provide a concrete example of an interacting higher-derivative system for which integrability and periodic classical solutions can be established in a fully explicit manner. |
| title | Conformal bi-Hamiltonian structure and integrability of an interacting Pais-Uhlenbeck oscillator |
| topic | Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2602.12858 |