Stability and bifurcations for the \(N+1\) vortex problem on the sphere

DOI10.1070/RD2003v008n03ABEH000243zbMath1150.76348OpenAlexW4230152212MaRDI QIDQ1876369

Hildeberto E. Cabral, Kenneth R. Meyer, Douglas C. Schmidt

Publication date: 6 September 2004

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rd2003v008n03abeh000243

zbMATH Keywords

bifurcationring of vorticesvortices at a fixed latitude

Mathematics Subject Classification ID

Vortex flows for incompressible inviscid fluids (76B47) Stability theory of functional-differential equations (34K20) Bifurcation theory of functional-differential equations (34K18)

Related Items (12)

Von Kármán vortex streets on the sphere ⋮ Existence and Stability of Four-Vortex Collinear Relative Equilibria with Three Equal Vorticities ⋮ TheN-vortex problem on a rotating sphere. I Multi-frequency configurations ⋮ On nonlinear stability of the regular vortex systems on a sphere ⋮ Chaotic motion of the \(N\)-vortex problem on a sphere. II. Saddle centers in three-degree-of-freedom Hamiltonians ⋮ Lyapunov orbits in the \(n\)-vortex problem on the sphere ⋮ Point vortex equilibria on the sphere via Brownian ratchets ⋮ Invariant dynamical systems embedded in the \(N\)-vortex problem on a sphere with pole vortices ⋮ Energy-momentum stability of icosahedral configurations of point vortices on a sphere ⋮ The N -vortex problem on a rotating sphere. III. Ring configurations coupled to a background field ⋮ Lyapunov orbits in the \(n\)-vortex problem ⋮ Chaotic motion of the \(N\)-vortex problem on a sphere. I. Saddle-centers in two-degree-of-freedom Hamiltonians

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