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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 
[1] 
Björn Gebhard. Periodic solutions for the Nvortex problem via a superposition principle. Discrete & Continuous Dynamical Systems  A, 2018, 38 (11) : 54435460. doi: 10.3934/dcds.2018240 
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P.K. Newton. Nvortex equilibrium theory. Discrete & Continuous Dynamical Systems  A, 2007, 19 (2) : 411418. doi: 10.3934/dcds.2007.19.411 
[3] 
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 & Optimization, 2020 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 & Continuous Dynamical Systems  A, 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 & Continuous Dynamical Systems  A, 2017, 37 (10) : 51635190. doi: 10.3934/dcds.2017224 
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Shaoyun Shi, Wenlei Li. Nonintegrability of generalized YangMills Hamiltonian system. Discrete & Continuous Dynamical Systems  A, 2013, 33 (4) : 16451655. doi: 10.3934/dcds.2013.33.1645 
[8] 
Joseph Nebus. The Dirichlet quotient of point vortex interactions on the surface of the sphere examined by Monte Carlo experiments. Discrete & Continuous Dynamical Systems  B, 2005, 5 (1) : 125136. doi: 10.3934/dcdsb.2005.5.125 
[9] 
Juan J. MoralesRuiz, Sergi Simon. On the meromorphic nonintegrability of some $N$body problems. Discrete & Continuous Dynamical Systems  A, 2009, 24 (4) : 12251273. doi: 10.3934/dcds.2009.24.1225 
[10] 
Younghun Hong. Strichartz estimates for $N$body Schrödinger operators with small potential interactions. Discrete & Continuous Dynamical Systems  A, 2017, 37 (10) : 53555365. doi: 10.3934/dcds.2017233 
[11] 
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] 
Xavier Perrot, Xavier Carton. Pointvortex interaction in an oscillatory deformation field: Hamiltonian dynamics, harmonic resonance and transition to chaos. Discrete & Continuous Dynamical Systems  B, 2009, 11 (4) : 971995. doi: 10.3934/dcdsb.2009.11.971 
[13] 
Guillaume Duval, Andrzej J. Maciejewski. Integrability of Hamiltonian systems with homogeneous potentials of degrees $\pm 2$. An application of higher order variational equations. Discrete & Continuous Dynamical Systems  A, 2014, 34 (11) : 45894615. doi: 10.3934/dcds.2014.34.4589 
[14] 
Mitsuru Shibayama. Nonintegrability criterion for homogeneous Hamiltonian systems via blowingup technique of singularities. Discrete & Continuous Dynamical Systems  A, 2015, 35 (8) : 37073719. doi: 10.3934/dcds.2015.35.3707 
[15] 
A. Ghose Choudhury, Partha Guha. Chiellini integrability condition, planar isochronous systems and Hamiltonian structures of Liénard equation. Discrete & Continuous Dynamical Systems  B, 2017, 22 (6) : 24652478. doi: 10.3934/dcdsb.2017126 
[16] 
Mitsuru Shibayama. Nonintegrability of the collinear threebody problem. Discrete & Continuous Dynamical Systems  A, 2011, 30 (1) : 299312. doi: 10.3934/dcds.2011.30.299 
[17] 
Zhong Tan, Jianfeng Zhou. Higher integrability of weak solution of a nonlinear problem arising in the electrorheological fluids. Communications on Pure & Applied Analysis, 2016, 15 (4) : 13351350. doi: 10.3934/cpaa.2016.15.1335 
[18] 
Petteri Piiroinen, Martin Simon. Probabilistic interpretation of the Calderón problem. Inverse Problems & Imaging, 2017, 11 (3) : 553575. doi: 10.3934/ipi.2017026 
[19] 
Yong Zhou, Jishan Fan. Regularity criteria of strong solutions to a problem of magnetoelastic interactions. Communications on Pure & Applied Analysis, 2010, 9 (6) : 16971704. doi: 10.3934/cpaa.2010.9.1697 
[20] 
Marius Cocou. A dynamic viscoelastic problem with friction and ratedepending contact interactions. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020060 
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