The birth of twin Poincaré-Birkhoff chains near 1:3 resonance

DOI10.1016/0378-4371(88)90007-6zbMath0683.58028OpenAlexW2127402816MaRDI QIDQ1824926

Yanyan Li

Publication date: 1988

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

Full work available at URL: https://research.utwente.nl/en/publications/the-birth-of-twin-poincarebirkhoff-chains-near-13-resonance(7b819cd0-eceb-462a-9d4b-7dbe9960c3c8).html

zbMATH Keywords

area-preserving mapPoincaré-Birkhoff theorem1:3 resonancebirth process of two twin Poincaré-Birkhoff chains

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Ergodic theory (37A99)

Related Items (13)

Nonmonotonic twist maps ⋮ Dimerized island chains in tokamaks ⋮ Area preserving nontwist maps: Periodic orbits and transition to chaos ⋮ On a new fixed point of the renormalization group operator for area-preserving maps ⋮ Threshold to global diffusion in a nonmonotonic map with quadratic nonlinearity. ⋮ Large-scale chaos for arbitrarily small perturbations in non-twist Hamiltonian systems. ⋮ Bifurcation-reconnection sequences in nonpendular resonance ⋮ Reconnection in a global model of Poincaré map describing dynamics of magnetic field lines in a reversed shear tokamak ⋮ Meanders and reconnection–collision sequences in the standard nontwist map ⋮ Twist singularities for symplectic maps ⋮ A simple reconnecting map ⋮ Bifurcation of periodic orbits near a frequency maximum in near- integrable driven oscillators with friction ⋮ DEGENERATE BIFURCATIONS OF RESONANT TORI IN HAMILTONIAN SYSTEMS

Cites Work

• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• The birth process of periodic orbits in non-twist maps
• Universal behaviour in families of area-preserving maps
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
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