Nonintegrability of dissipative planar systems. (English) Zbl 07855421
Summary: We consider dissipative autonomous perturbations of planar Hamiltonian systems and give a sufficient condition for them not to be complex-meromorphically Bogoyavlenskij-integrable such that the first integral or commutative vector field also depends complex-meromorphically on the small parameter. We illustrate the theoretical result for three examples including systems with the Morse potential and effective potential of the Kepler problem.
MSC:
| 37J30 | Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) |
| 12H05 | Differential algebra |
| 70F05 | Two-body problems |
Keywords:
nonintegrability; dissipative planar system; perturbation; Morales-Ramis theory; Melnikov functionReferences:
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