A geometric singular perturbation theory approach to constrained differential equations |
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Authors: | Pedro Toniol Cardin Marco Antonio Teixeira |
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Abstract: | This paper is concerned with a geometric study of ()‐parameter families of constrained differential systems, where . Our main results say that the dynamics of such a family close to the impasse set is equivalent to the dynamics of a multiple time scale singular perturbation problem (that is a singularly perturbed system containing several small parameters). This enables us to use a geometric theory for multiscale systems in order to describe the behaviour of such a family close to the impasse set. We think that a systematic program towards a combination between geometric singular perturbation theory and constrained systems and problems involving persistence of typical minimal sets are currently emergent. Some illustrations and applications of the main results are provided. |
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Keywords: | constrained systems multiple time scales singular perturbation problems 34C05 34D15 37C10 |
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