Point vortices on the hyperbolic plane

James Montaldi; Citlalitl Nava-Gaxiola

doi:10.1063/1.4897210

Point vortices on the hyperbolic plane

James Montaldi, Citlalitl Nava-Gaxiola

Research output: Contribution to journal › Article › peer-review

Abstract

© 2014 AIP Publishing LLC.We investigate the dynamical system of point vortices on the hyperboloid. This system has non-compact symmetry SL(2, R) and a coadjoint equivariant momentum map. The relative equilibrium conditions are found and the trajectories of relative equilibria with non-zero momentum value are described. We also provide the classification of relative equilibria and the stability criteria for a number of cases, focusing on 2 and 3 vortices. Unlike the system on the sphere, this system has relative equilibria with non-compact momentum isotropy subgroup, and these are used to illustrate the different stability types of relative equilibria.

Original language	English
Article number	102702
Pages (from-to)	1-14
Number of pages	13
Journal	Journal of Mathematical Physics
Volume	55
Issue number	10
DOIs	https://doi.org/10.1063/1.4897210
Publication status	Published - 6 Oct 2014

Keywords

vortices, hamiltonian system with symmetry, stability, relative equilibria

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10.1063/1.4897210Licence: CC BY-NC

http://scitation.aip.org/content/aip/journal/jmpLicence: CC BY-NC

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title = "Point vortices on the hyperbolic plane",

abstract = "{\textcopyright} 2014 AIP Publishing LLC.We investigate the dynamical system of point vortices on the hyperboloid. This system has non-compact symmetry SL(2, R) and a coadjoint equivariant momentum map. The relative equilibrium conditions are found and the trajectories of relative equilibria with non-zero momentum value are described. We also provide the classification of relative equilibria and the stability criteria for a number of cases, focusing on 2 and 3 vortices. Unlike the system on the sphere, this system has relative equilibria with non-compact momentum isotropy subgroup, and these are used to illustrate the different stability types of relative equilibria.",

keywords = "vortices, hamiltonian system with symmetry, stability, relative equilibria",

author = "James Montaldi and Citlalitl Nava-Gaxiola",

note = "C N-G was supported by CONACyT grant 307762.",

year = "2014",

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Y1 - 2014/10/6

N2 - © 2014 AIP Publishing LLC.We investigate the dynamical system of point vortices on the hyperboloid. This system has non-compact symmetry SL(2, R) and a coadjoint equivariant momentum map. The relative equilibrium conditions are found and the trajectories of relative equilibria with non-zero momentum value are described. We also provide the classification of relative equilibria and the stability criteria for a number of cases, focusing on 2 and 3 vortices. Unlike the system on the sphere, this system has relative equilibria with non-compact momentum isotropy subgroup, and these are used to illustrate the different stability types of relative equilibria.

AB - © 2014 AIP Publishing LLC.We investigate the dynamical system of point vortices on the hyperboloid. This system has non-compact symmetry SL(2, R) and a coadjoint equivariant momentum map. The relative equilibrium conditions are found and the trajectories of relative equilibria with non-zero momentum value are described. We also provide the classification of relative equilibria and the stability criteria for a number of cases, focusing on 2 and 3 vortices. Unlike the system on the sphere, this system has relative equilibria with non-compact momentum isotropy subgroup, and these are used to illustrate the different stability types of relative equilibria.

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SP - 1

EP - 14

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 10

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ER -

Point vortices on the hyperbolic plane

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