A geometric singular perturbation theory approach to constrained differential equations. Issue 4 (13th November 2018)

• Record Type: Journal Article
• Authors: Toniol Cardin, Pedro; Teixeira, Marco Antonio
• Is Part Of: Mathematische Nachrichten. Volume 292:Issue 4(2019)
• Page Start: 892
• Page End: 904
• Publication Date: 2018-11-13
• Subjects: constrained systems -- multiple time scales -- singular perturbation problems -- 34C05 -- 34D15 -- 37C10; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201700444
• Languages: English
• ISSNs: 0025-584X

Abstract

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.