Implicit differential equations with impasse singularities and singular perturbation problems

Author(s)

Cardin, Pedro Toniol ^[1] ; da Silva, Paulo Ricardo ^[1] ; Teixeira, Marco Antonio ^[2]

Affiliation

^[1] IBILCE UNESP, Dept Matemat, BR-15054000 Sao Paulo - Brazil

^[2] IMECC UNICAMP, BR-13081970 Campinas, SP - Brazil

• Document type: Journal article
• Source: Israel Journal of Mathematics; v. 189, n. 1, p. 307-322, JUN 2012.
• Web of Science Citations: 2

Abstract

This paper concerns families of constrained differential systems having the form [fx1-1] where h: a{''}e (n) -> a{''}e is a C (r) -function, (alpha (1), aEuro broken vertical bar, alpha (n) ) is a C (r) vector field on a{''}e (n) , r a parts per thousand yen 1, x a a{''}e (n) and lambda is a real parameter. Using singular perturbation techniques we present some results on the dynamics of the system around a point (x, lambda) of the impasse set lambda = h(x). In addition, planar constrained systems with non-regular impasse surfaces are considered. (AU)

• FAPESP's process: 07/06896-5 - Geometry of control, dynamical and stochastic systems
• Grantee: Luiz Antonio Barrera San Martin
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 07/07957-8 - Differential equations with impasses and singular perturbation
• Grantee: Pedro Toniol Cardin
• Support Opportunities: Scholarships in Brazil - Doctorate