平面分段光滑向量场正测度极小集上的几何奇异摄动

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems Pub Date : 2025-09-01 DOI:10.1016/j.nahs.2025.101628

Tiago Carvalho , Luiz Fernando Gonçalves , Bruno Rodrigues Freitas

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引用次数: 0

摘要

本文利用奇异摄动的几何理论，对一类具有正测度极小集的分段光滑向量场进行了详细的研究。在我们的分析中使用的规范形式代表了更大的一类分段光滑系统，包括不连续谐振子的模型。通过一个去广域化过程，该过程需要应用一个n-正则化函数以及连续的加权爆炸（定向的，球面的和极的），我们得到了去广域化向量场Zω轨迹的吸引子。

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

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

C^{n}

-regularization function along with successive weighted blow-ups (directional, spherical and polar), we obtain an attractor for the trajectories of the desingularized vector field

Z_{ω}

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来源期刊

Nonlinear Analysis-Hybrid Systems AUTOMATION & CONTROL SYSTEMS-MATHEMATICS, APPLIED

CiteScore

8.30

自引率

9.50%

发文量

审稿时长

>12 weeks

期刊介绍： Nonlinear Analysis: Hybrid Systems welcomes all important research and expository papers in any discipline. Papers that are principally concerned with the theory of hybrid systems should contain significant results indicating relevant applications. Papers that emphasize applications should consist of important real world models and illuminating techniques. Papers that interrelate various aspects of hybrid systems will be most welcome.