Quasi-periodic Swing via Weak KAM Theory
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912436709228544 |
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| author | Niu, Xun Wang, Kaizhi Li, Yong |
| author_facet | Niu, Xun Wang, Kaizhi Li, Yong |
| contents | We investigate the dynamics of the quasi-periodic swing equations from the perspective of weak KAM theory. To this end, we firstly study a class of Hamiltonian systems. We obtain that the limit $u$, which derived from convergence of a sequence of functional minimizers, satisfies Hamilton-Jacobi equations in a weak sense. This is the so-called weak KAM solution. Meanwhile, we also get aminimal measures $μ$. Finally, we derive that the existence of weak KAM solutions for the swing equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01322 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quasi-periodic Swing via Weak KAM Theory Niu, Xun Wang, Kaizhi Li, Yong Dynamical Systems We investigate the dynamics of the quasi-periodic swing equations from the perspective of weak KAM theory. To this end, we firstly study a class of Hamiltonian systems. We obtain that the limit $u$, which derived from convergence of a sequence of functional minimizers, satisfies Hamilton-Jacobi equations in a weak sense. This is the so-called weak KAM solution. Meanwhile, we also get aminimal measures $μ$. Finally, we derive that the existence of weak KAM solutions for the swing equations. |
| title | Quasi-periodic Swing via Weak KAM Theory |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2312.01322 |