Nonintegrability of dissipative planar systems

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. •Dissipative autonomous perturbations of planar Hamiltonian systems are studied.•A technique to prove their meromorphic Bogoyavlenskij-nonintegrability is proposed.•It is successfully applied to three examples.•They include systems with the Morse and Kepler effective potential.