Self-intersection of the complex separatrices and the nonexistence of the integrals in the Hamiltonian systems with one-and-half degrees of freedom

DOI10.1016/0021-8928(81)90075-7zbMath0503.70012OpenAlexW1970463641MaRDI QIDQ1173418

S. L. Ziglin

Publication date: 1981

Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8928(81)90075-7

zbMATH Keywords

analytically dependent on parameteremergent complex separatrixno analytic first integralone-and-half degreesuniversal intersections

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Local and nonlocal bifurcation theory for dynamical systems (37G99) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (10)

The splitting of separatrices, the branching of solutions, and nonintegrability of many-dimensional systems. application to the problem of the motion of a spherical pendulum with an oscillating suspension point ⋮ Nonintegrability of nearly integrable dynamical systems near resonant periodic orbits ⋮ Unnamed Item ⋮ Nonintegrability of forced nonlinear oscillators ⋮ Obstructions to integrability of nearly integrable dynamical systems near regular level sets ⋮ On the integrability of a system describing the stationary solutions in Bose-Fermi mixtures ⋮ Persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems ⋮ Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I ⋮ Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II ⋮ Symbolic Software for the Painlevé Test of Nonlinear Ordinary and Partial Differential Equations

Cites Work

• Unnamed Item
• Nonexistence of univalued integrals and branching of solutions in solid body dynamics
• The analytic invariants of an area-preserving mapping near a hyperbolic fixed point

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