Aref, H.; Pomphrey, N. Integrable and chaotic motions of four vortices. I: The case of identical vortices. (English) Zbl 0483.76031 Proc. R. Soc. Lond., Ser. A 380, 359-387 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 38 Documents MSC: 76B47 Vortex flows for incompressible inviscid fluids 70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics 70H05 Hamilton’s equations 70K99 Nonlinear dynamics in mechanics 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics 33E05 Elliptic functions and integrals 76M99 Basic methods in fluid mechanics Keywords:three-vortex problem; two-dimensional; sequence of canonical transformations; N-degree-of-freedom Hamiltonian; N identical vortices; reduction procedure; coupled nonlinear oscillators; heteroclinic orbit in phase space; integrability of Euler’s equation; Poisson-bracket formalism; point vortices PDFBibTeX XMLCite \textit{H. Aref} and \textit{N. Pomphrey}, Proc. R. Soc. Lond., Ser. A 380, 359--387 (1982; Zbl 0483.76031) Full Text: DOI