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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Fenichel Theory for Multiple Time Scale Singular Perturbation Problems

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Cardin, Pedro Toniol [1] ; Teixeira, Marco Antonio [2]
Total Authors: 2
[1] Univ Estadual Paulista UNESP, Fac Engn Ilha Solteira, Dept Matemat, Rua Rio de Janeiro 266, BR-15385000 Ilha Solteira, SP - Brazil
[2] Univ Estadual Campinas UNICAMP, Inst Matemat Estat & Comp Cient, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS; v. 16, n. 3, p. 1425-1452, 2017.
Web of Science Citations: 4

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 RI, 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. (AU)

FAPESP's process: 13/24541-0 - Ergodic and qualitative theory of dynamical systems
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 13/21947-6 - Geometric theory of the singularly perturbed differential equations
Grantee:Pedro Toniol Cardin
Support Opportunities: Regular Research Grants
FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
Grantee:Marco Antônio Teixeira
Support Opportunities: Research Projects - Thematic Grants