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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 Nvortex problem: I. Integrability
1.  Department of Aerospace & Mechanical Engineering and Department of Mathematics, University of Southern California, Los Angeles, CA 900891191, United States, United States, United States 
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Björn Gebhard. Periodic solutions for the Nvortex problem via a superposition principle. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 54435460. doi: 10.3934/dcds.2018240 
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P.K. Newton. Nvortex equilibrium theory. Discrete and Continuous Dynamical Systems, 2007, 19 (2) : 411418. doi: 10.3934/dcds.2007.19.411 
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Carlos GarcíaAzpeitia. Relative periodic solutions of the $ n $vortex problem on the sphere. Journal of Geometric Mechanics, 2019, 11 (3) : 427438. doi: 10.3934/jgm.2019021 
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Mohsen Abdolhosseinzadeh, Mir Mohammad Alipour. Design of experiment for tuning parameters of an ant colony optimization method for the constrained shortest Hamiltonian path problem in the grid networks. Numerical Algebra, Control and Optimization, 2021, 11 (2) : 321332. doi: 10.3934/naco.2020028 
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Nicolas Forcadel, Cyril Imbert, Régis Monneau. Homogenization of some particle systems with twobody interactions and of the dislocation dynamics. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 785826. doi: 10.3934/dcds.2009.23.785 
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Božidar Jovanović, Vladimir Jovanović. Virtual billiards in pseudo–euclidean spaces: Discrete hamiltonian and contact integrability. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 51635190. doi: 10.3934/dcds.2017224 
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Shaoyun Shi, Wenlei Li. Nonintegrability of generalized YangMills Hamiltonian system. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 16451655. 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, 2022, 27 (8) : 43054316. doi: 10.3934/dcdsb.2021228 
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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) : 125136. doi: 10.3934/dcdsb.2005.5.125 
[10] 
Juan J. MoralesRuiz, Sergi Simon. On the meromorphic nonintegrability of some $N$body problems. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 12251273. doi: 10.3934/dcds.2009.24.1225 
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Vladimir S. Gerdjikov, Rossen I. Ivanov, Aleksander A. Stefanov. RiemannHilbert problem, integrability and reductions. Journal of Geometric Mechanics, 2019, 11 (2) : 167185. doi: 10.3934/jgm.2019009 
[12] 
Younghun Hong. Strichartz estimates for $N$body Schrödinger operators with small potential interactions. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 53555365. doi: 10.3934/dcds.2017233 
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Marco Di Francesco, Serikbolsyn Duisembay, Diogo Aguiar Gomes, Ricardo Ribeiro. Particle approximation of onedimensional MeanFieldGames with local interactions. Discrete and Continuous Dynamical Systems, 2022, 42 (7) : 35693591. doi: 10.3934/dcds.2022025 
[14] 
Xavier Perrot, Xavier Carton. Pointvortex interaction in an oscillatory deformation field: Hamiltonian dynamics, harmonic resonance and transition to chaos. Discrete and Continuous Dynamical Systems  B, 2009, 11 (4) : 971995. 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) : 45894615. doi: 10.3934/dcds.2014.34.4589 
[16] 
Mitsuru Shibayama. Nonintegrability criterion for homogeneous Hamiltonian systems via blowingup technique of singularities. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 37073719. doi: 10.3934/dcds.2015.35.3707 
[17] 
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) : 24652478. doi: 10.3934/dcdsb.2017126 
[18] 
Mitsuru Shibayama. Nonintegrability of the collinear threebody problem. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 299312. 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) : 13351350. doi: 10.3934/cpaa.2016.15.1335 
[20] 
Yong Zhou, Jishan Fan. Regularity criteria of strong solutions to a problem of magnetoelastic interactions. Communications on Pure and Applied Analysis, 2010, 9 (6) : 16971704. doi: 10.3934/cpaa.2010.9.1697 
2021 Impact Factor: 1.497
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