Invariant manifolds and limit periodic sets of discontinuous foliations
Regularization of planar Filippov Systems near a codimension one singularity
| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] UHA, Lab Mathemat Informat & Applicat, 4 Rue Freres Lumiere, F-68093 Mulhouse - France
[2] Univ Strasbourg, Strasbourg - France
[3] Univ Estadual Paulista, IBILCE, Dept Matemat, Rua C Colombo, 2265, BR-15054000 Sao Paulo - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 263, n. 12, p. 8362-8390, DEC 15 2017. |
| Web of Science Citations: | 3 |
| Abstract | |
We study the regularization of an oriented 1-foliation F on M \textbackslash{} Sigma where M is a smooth manifold and Sigma subset of M is a closed subset, which can be interpreted as the discontinuity locus of F. In the spirit of Filippov's work, we define a sliding and sewing dynamics on the discontinuity locus Sigma as some sort of limit of the dynamics of a nearby smooth 1-foliation and obtain conditions to identify whether a point belongs to the sliding or sewing regions. (C) 2017 Elsevier Inc. All rights reserved. (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: | 16/02031-9 - Regularization of discontinuously foliated manifolds |
| Grantee: | Paulo Ricardo da Silva |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |