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A successive continuation method for locating connecting orbits in parametrized systems of autonomous ODEs was considered in [Numer. Algorithms, 14 (1997), pp. 103--124]. In this paper we present an improved algorithm for locating and continuing connecting orbits, which includes a new algorithm for the continuation of invariant subspaces. The latter algorithm is of independent interest and can be used in contexts different than the present one.
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Demmel et al. (2000) studied this question.
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