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Geometric singular perturbation on a positive measure minimal set of a planar piecewise smooth vector field

delete2025-09-01
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PRE
AI
C
Carvalho, Tiago *
L
Luiz Fernando Gonçalves
B
Bruno Rodrigues de Freitas
DOI：10.1016/j.nahs.2025.101628delete
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Abstract

Abstract

En 中文
In this paper, we employ the geometric theory of singular perturbations to obtain detailed insights concerning a class of piecewise smooth vector fields exhibiting a positive measure minimal set. The canonical form used in our analysis represents a larger class of piecewise smooth systems, encompassing models of discontinuous harmonic oscillators. Through a desingularization process, which entails the application of a Cn-regularization function along with successive weighted blow-ups (directional, spherical and polar), we obtain an attractor for the trajectories of the desingularized vector field Zω.
Keywords:
singular perturbations
piecewise smooth vector fields
desingularization
blow-up method
attractor

Journal

N
Nonlinear Analysis and Hybrid Systems
IF:
4.1
Papers:
1.4K
Citations:
3.1K

Organization

I
Institute of Biosciences
Scholars:
177
Papers: 84
Citations: 1
I
Institute of Mathematics and Statistics
Scholars:
22
Papers: 20
Citations: 0
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