Slow divergence integral in regularized piecewise smooth systems
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866918110592761856 |
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| author | Huzak, Renato Kristiansen, Kristian Uldall Radunović, Goran |
| author_facet | Huzak, Renato Kristiansen, Kristian Uldall Radunović, Goran |
| contents | In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain diverse tangency points. We show that the slow divergence integral is invariant under smooth equivalences. This is a natural generalization of the notion of slow divergence integral along normally hyperbolic portions of curve of singularities in smooth planar slow-fast systems. We give an interesting application of the integral in a model with visible-invisible two-fold of type $VI_3$. It is related to a connection between so-called Minkowski dimension of bounded and monotone "entry-exit" sequences and the number of sliding limit cycles produced by so-called canard cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06719 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Slow divergence integral in regularized piecewise smooth systems Huzak, Renato Kristiansen, Kristian Uldall Radunović, Goran Dynamical Systems 34E15, 34E17, 34C40 In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain diverse tangency points. We show that the slow divergence integral is invariant under smooth equivalences. This is a natural generalization of the notion of slow divergence integral along normally hyperbolic portions of curve of singularities in smooth planar slow-fast systems. We give an interesting application of the integral in a model with visible-invisible two-fold of type $VI_3$. It is related to a connection between so-called Minkowski dimension of bounded and monotone "entry-exit" sequences and the number of sliding limit cycles produced by so-called canard cycles. |
| title | Slow divergence integral in regularized piecewise smooth systems |
| topic | Dynamical Systems 34E15, 34E17, 34C40 |
| url | https://arxiv.org/abs/2310.06719 |