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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2202.06160 |
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| _version_ | 1866915798568665088 |
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| author | Balabanova, Nataliya A. Montaldi, James |
| author_facet | Balabanova, Nataliya A. Montaldi, James |
| contents | We investigate the motion of point vortices on the Mobius band and Klein bottle. Since these are non-orientable surfaces, the standard Hamiltonian approach does not apply. We therefore begin by establishing a modified Hamiltonian approach which works for arbitrary non-orientable surfaces, through describing the phase space, the Hamiltonian and the local equations of motion. We use a combination of twisted functions and oriented double covers to adapt some of the known notions of vortex dynamics to non-orientable surfaces. For both of the surfaces of interest, we write Hamiltonian-type equations of vortex motion explicitly and follow that by the description of relative equilibria and an investigation of the motion of one and two vortices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_06160 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Hamiltonian approach for point vortices on non-orientable surfaces Balabanova, Nataliya A. Montaldi, James Dynamical Systems We investigate the motion of point vortices on the Mobius band and Klein bottle. Since these are non-orientable surfaces, the standard Hamiltonian approach does not apply. We therefore begin by establishing a modified Hamiltonian approach which works for arbitrary non-orientable surfaces, through describing the phase space, the Hamiltonian and the local equations of motion. We use a combination of twisted functions and oriented double covers to adapt some of the known notions of vortex dynamics to non-orientable surfaces. For both of the surfaces of interest, we write Hamiltonian-type equations of vortex motion explicitly and follow that by the description of relative equilibria and an investigation of the motion of one and two vortices. |
| title | A Hamiltonian approach for point vortices on non-orientable surfaces |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2202.06160 |