Non-integrability of the 4-vortex system: Analytical proof

DOI10.1007/BF01260390zbMath0825.58013OpenAlexW1979614680MaRDI QIDQ1812532

Sônia Pinto de Carvalho, Jair Koiller

Publication date: 25 June 1992

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01260390

zbMATH Keywords

horseshoeMelnikov methoddynamics of 4 point vortices

Mathematics Subject Classification ID

Vortex flows for incompressible inviscid fluids (76B47) Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (14)

Integrability of point-vortex dynamics via symplectic reduction: a survey ⋮ A combinatorial perturbation method and Arnold's whiskered tori in vortex dynamics ⋮ On the motion of two-dimensional vortices with mass ⋮ Relative equilibria of the \((1+N)\)-vortex problem ⋮ Relative periodic solutions of the \(N\)-vortex problem via the variational method ⋮ Stability of the rhombus vortex problem with a central vortex ⋮ The N-vortex problem on a symmetric ellipsoid: A perturbation approach ⋮ Integrability and chaos in vortex lattice dynamics ⋮ Unnamed Item ⋮ The \(n\)-vortex problem on a Riemann sphere ⋮ Dynamics of restricted three and four vortices problem on the plane ⋮ Bifurcations and Chaos in the Dynamics of Two Point Vortices in an Acoustic Wave ⋮ Dynamics of two moving vortices in the presence of a fixed vortex ⋮ Compatibility of symplectic structures adapted to noncommutatively integrable systems

Cites Work

• Unnamed Item
• Lagrangian submanifolds and Hamiltonian systems
• Quasi-periodic motions of vortex systems
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Concerning the paper Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom by P. J. Holmes and J. E. Marsden
• Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom
• Integrability and non-integrability in Hamiltonian mechanics
• The restricted problem of n+? bodies
• Integrable, Chaotic, and Turbulent Vortex Motion in Two-Dimensional Flows
• Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems
• Transversal Homoclinic Orbits in an Integrable System

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