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Global Phase Diagrams of Three Point Vortices

School of Mathematics and Computing Sciences, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541002, P. R. China

E-mail Address: luoqian199811@163.com

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Yufei Chen

School of Mathematics and Computing Sciences, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541002, P. R. China

E-mail Address: chenyufeiff@163.com

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, and

Qihuai Liu

https://orcid.org/0000-0002-1661-5670

School of Mathematics and Computing Sciences, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541002, P. R. China

Center for Applied Mathematics of Guangxi, (Guangxi Normal University), Guilin 541004, P. R. China

E-mail Address: qhuailiu@gmail.com

Corresponding author.

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https://doi.org/10.1142/S0218127422500250Cited by:5 (Source: Crossref)

Abstract

In this paper, we investigate the dynamics of three-vortex systems and give a global phase diagram analysis with different types of parameters on the plane. By using the invariants to construct canonical transformations, the Hamiltonian of the three-vortex system is reduced to a desired two-dimensional Hamiltonian. Then, we analyze its phase diagrams by considering all possible situations. In each case, the stabilities of the equilibrium points and singular points are established by using numerical methods, and we obtain the distribution of trajectories in the phase space.

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Vol. 32, No. 02

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Received 29 July 2021

Revised 5 October 2021

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Global Phase Diagrams of Three Point Vortices

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