Periodic trajectories for a two-dimensional nonintegrable Hamiltonian

DOI10.1016/0003-4916(87)90123-0zbMath0637.70019OpenAlexW2067296641MaRDI QIDQ1098659

K. T. R. Davies, Michel Baranger

Publication date: 1987

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0003-4916(87)90123-0

zbMATH Keywords

monodromy matrixbranchingsstability propertiesnumerical studyperiod-doublingsclassical periodic trajectoriesisochronous branchingsperiod-multiplyings of higher ordersregular regions of phase spacestable periodic trajectoriessymmetry of the Hamiltoniantwo-dimensional, nonintegrable Hamiltonian

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Stability theory for smooth dynamical systems (37C75) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (13)

Calculations of periodic trajectories for the Hénon–Heiles Hamiltonian using the monodromy method ⋮ Periodic orbits of nonscaling Hamiltonian systems from quantum mechanics ⋮ Bifurcations of periodic trajectories in non-integrable Hamiltonian systems with two degrees of freedom: Numerical and analytical results ⋮ Invariant tori for two-dimensional non-integrable Hamiltonians ⋮ The calculation of periodic trajectories ⋮ Semiclassical approximation of the Wigner function for the canonical ensemble ⋮ Husimi–Wigner representation of chaotic eigenstates ⋮ Complex dynamics of some Hamiltonian systems: nonintegrability of equations of motion ⋮ Periodic librations and their effect on the quantum energy spectrum ⋮ Semiclassical limit for a truncated Hamiltonian ⋮ Semiclassical structure of trace formulas ⋮ Solving the boundary value problem for finite Kirchhoff rods ⋮ Calculations of periodic orbits: The monodromy method and application to regularized systems

Cites Work

• Universal behaviour in families of area-preserving maps
• Stochastic behavior in classical and quantum Hamiltonian systems. Volta memorial conference, Como, 1977
• Generic Bifurcation of Periodic Points
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