A generalized Poincaré-Birkhoff theorem with applications to coaxial vortex ring motion

DOI10.3934/dcdsb.2005.5.15zbMath1075.37018OpenAlexW2082694055MaRDI QIDQ1772478

Chengwen Wang, Jyoti A. Champanerkar, D. L. Blackmore

Publication date: 18 April 2005

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2005.5.15

zbMATH Keywords

Hamiltonian systemsKAM theoryLefschetz numbersymplectic mapsfixed-points

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Vortex flows for incompressible inviscid fluids (76B47) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

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The dynamics of vortex rings: leapfrogging, choreographies and the stability problem ⋮ Pitchfork bifurcations of invariant manifolds ⋮ Coaxial axisymmetric vortex rings: 150 years after Helmholtz ⋮ A coaxial vortex ring model for vortex breakdown

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