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The Dirichlet quotient of point vortex interactions on the surface of the sphere examined by Monte Carlo experiments
The constrained planar N-vortex problem: I. Integrability
1. | Department of Aerospace & Mechanical Engineering and Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1191, United States, United States, United States |
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Björn Gebhard. Periodic solutions for the N-vortex problem via a superposition principle. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 5443-5460. doi: 10.3934/dcds.2018240 |
[2] |
P.K. Newton. N-vortex equilibrium theory. Discrete and Continuous Dynamical Systems, 2007, 19 (2) : 411-418. doi: 10.3934/dcds.2007.19.411 |
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Carlos García-Azpeitia. Relative periodic solutions of the $ n $-vortex problem on the sphere. Journal of Geometric Mechanics, 2019, 11 (3) : 427-438. doi: 10.3934/jgm.2019021 |
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Shaoyun Shi, Wenlei Li. Non-integrability of generalized Yang-Mills Hamiltonian system. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1645-1655. doi: 10.3934/dcds.2013.33.1645 |
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Jaume Llibre, Yuzhou Tian. Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021228 |
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Juan J. Morales-Ruiz, Sergi Simon. On the meromorphic non-integrability of some $N$-body problems. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1225-1273. doi: 10.3934/dcds.2009.24.1225 |
[10] |
Joseph Nebus. The Dirichlet quotient of point vortex interactions on the surface of the sphere examined by Monte Carlo experiments. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 125-136. doi: 10.3934/dcdsb.2005.5.125 |
[11] |
Vladimir S. Gerdjikov, Rossen I. Ivanov, Aleksander A. Stefanov. Riemann-Hilbert problem, integrability and reductions. Journal of Geometric Mechanics, 2019, 11 (2) : 167-185. doi: 10.3934/jgm.2019009 |
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Younghun Hong. Strichartz estimates for $N$-body Schrödinger operators with small potential interactions. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5355-5365. doi: 10.3934/dcds.2017233 |
[13] |
Marco Di Francesco, Serikbolsyn Duisembay, Diogo Aguiar Gomes, Ricardo Ribeiro. Particle approximation of one-dimensional Mean-Field-Games with local interactions. Discrete and Continuous Dynamical Systems, 2022, 42 (7) : 3569-3591. doi: 10.3934/dcds.2022025 |
[14] |
Xavier Perrot, Xavier Carton. Point-vortex interaction in an oscillatory deformation field: Hamiltonian dynamics, harmonic resonance and transition to chaos. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 971-995. doi: 10.3934/dcdsb.2009.11.971 |
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Guillaume Duval, Andrzej J. Maciejewski. Integrability of Hamiltonian systems with homogeneous potentials of degrees $\pm 2$. An application of higher order variational equations. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4589-4615. doi: 10.3934/dcds.2014.34.4589 |
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Mitsuru Shibayama. Non-integrability criterion for homogeneous Hamiltonian systems via blowing-up technique of singularities. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3707-3719. doi: 10.3934/dcds.2015.35.3707 |
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A. Ghose Choudhury, Partha Guha. Chiellini integrability condition, planar isochronous systems and Hamiltonian structures of Liénard equation. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2465-2478. doi: 10.3934/dcdsb.2017126 |
[18] |
Mitsuru Shibayama. Non-integrability of the collinear three-body problem. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 299-312. doi: 10.3934/dcds.2011.30.299 |
[19] |
Zhong Tan, Jianfeng Zhou. Higher integrability of weak solution of a nonlinear problem arising in the electrorheological fluids. Communications on Pure and Applied Analysis, 2016, 15 (4) : 1335-1350. doi: 10.3934/cpaa.2016.15.1335 |
[20] |
Yong Zhou, Jishan Fan. Regularity criteria of strong solutions to a problem of magneto-elastic interactions. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1697-1704. doi: 10.3934/cpaa.2010.9.1697 |
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