Fenichel theory for multiple time scale singular perturbation problems

• Autor(a) principal: Cardin, Pedro Toniol [UNESP]
• Data de Publicação: 2017
• Outros Autores: Teixeira, Marco Antonio
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1137/16M1067202; http://hdl.handle.net/11449/175363
• topic: Fenichel theory; Multiple time scales; Singular perturbation

This paper is concerned with a geometric study of singularly perturbed systems of ordinary differential equations expressed by (n-1)-parameter families of smooth vector fields on ℝl, where n ≥ 2. The inherent characteristic of such systems is the presence of an arbitrary number n of time scales. For n = 2, the proposed geometric approach in this paper reports to Fenichel theory of fast-slow systems [N. Fenichel, J. Differential Equations, 31 (1979), pp. 53-98]. We extend the three main theorems due to Fenichel [N. Fenichel, J. Differential Equations, 31 (1979), pp. 53-98] to systems involving any number of time scales.