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It is argued that, if a regular Hamiltonian is perturbed by a term that produces chaos, the onset of chaos is shifted towards larger values of the perturbation parameter if the unperturbed spectrum is degenerate and the lifting of the degeneracy is of second order in this parameter. The argument is based on the behaviour of the exceptional points of the full problem.doi:10.1103/physreve.52.4762 pmid:9963973 fatcat:uvol5ms7gjarfhrwczakvaws2m