Abstract
We consider degenerate solutions on families of periodic solutions to ordinary differential equations. Degeneracy is understood as an arbitrary property of a solution that isolates this solution from generic cases. This can be either a bifurcation on a family or some topological peculiarity of the family, which causes a failure of a numerical algorithm applicable to generic cases. We suggest a means to compute these singular solutions with application of variational equations of higher order and with the same accuracy as ordinary solutions. The method is based on a symbolic recursive differentiation of an ODE with respect to initial values and parameters.
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