| Grant number: | 16/02031-9 |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| Start date: | September 03, 2016 |
| End date: | October 01, 2016 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Principal Investigator: | Paulo Ricardo da Silva |
| Grantee: | Paulo Ricardo da Silva |
| Visiting researcher: | Daniel Cantergiani Panazzolo |
| Visiting researcher institution: | Université de Haute-Alsace , France |
| Host Institution: | Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil |
| City of the host institution: | São José do Rio Preto |
| Associated research grant: | 13/24541-0 - Ergodic and qualitative theory of dynamical systems, AP.TEM |
Abstract
A finite set of vector fields, defines a piecewise-smooth vector field X on a manifold M and switching set E. A regularization is a 1-parameter family of smooth vector fields, converging to X, when the parameter goes to zero.We study regularization processes when the switching set is a regular surface and when its singular set is not empty. We introduce the concept of discontinuously foliated manifold and regularization of piecewise smooth oriented 1-foliation.The regularization processes studied are of the kinds Filippov, Nonlinear and the blow-up.We show that the regularization of the kind blow up gives a manifold on whichthe singular fiber has an invariant manifold S. The reduced flow on Sis equivalent to the sliding flow when S is normally hyperbolic. The case where S it is not normally hyperbolic appears when non Filippov regularizations are considered. (AU)
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