A geometric singular perturbation theory approach to constrained differential equations

Pedro Toniol Cardin and Marco Antonio Teixeira

Mathematische Nachrichten, 2019, vol. 292, issue 4, 892-904

Abstract: This paper is concerned with a geometric study of (n−1)‐parameter families of constrained differential systems, where n≥2. 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.

Date: 2019
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https://doi.org/10.1002/mana.201700444

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