Invariant dynamical systems embedded in the \(N\)-vortex problem on a sphere with pole vortices

DOI10.1016/j.physd.2006.04.002zbMath1091.76010OpenAlexW2023402841MaRDI QIDQ2495444

Takashi Sakajo

Publication date: 30 June 2006

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2115/8557

zbMATH Keywords

reduction methodshift transformationpolygonal ring configuration

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Vortex flows for incompressible inviscid fluids (76B47)

Related Items (4)

Chaotic motion of the \(N\)-vortex problem on a sphere. II. Saddle centers in three-degree-of-freedom Hamiltonians ⋮ From generation to chaotic motion of a ring configuration of vortex structures on a sphere ⋮ Toroidal geometry stabilizing a latitudinal ring of point vortices on a torus ⋮ Chaotic motion of the \(N\)-vortex problem on a sphere. I. Saddle-centers in two-degree-of-freedom Hamiltonians

Cites Work

• Stability and bifurcations for the \(N+1\) vortex problem on the sphere
• Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices
• The motion of three point vortices on a sphere
• Motion of a vortex sheet on a sphere with pole vortices
• The stability and energetics of corotating uniform vortices
• Relative equilibria of symmetricn-body problems on a sphere: Inverse and direct results
• Wave and vortex dynamics on the surface of a sphere
• Nonlinear Stability of a Latitudinal Ring of Point-Vortices on a Nonrotating Sphere
• Periodic motions of vortices on surfaces with symmetry
• Relative periodic orbits in point vortex systems
• Point vortices on a sphere: Stability of relative equilibria
• Stability of Relative Equilibria in the Problem of N+1 Vortices
• High-dimensional heteroclinic and homoclinic connections in odd point-vortex ring on a sphere
• On nonlinear stability of the regular vortex systems on a sphere
• The \(N\)-vortex problem. Analytical techniques

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