Cyclicity of sliding cycles with singularities of regularized piecewise smooth visible-invisible two-folds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910874032144384 |
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| author | Huang, Jicai Huzak, Renato Perez, Otavio Henrique Yao, Jinhui |
| author_facet | Huang, Jicai Huzak, Renato Perez, Otavio Henrique Yao, Jinhui |
| contents | In this paper we study the cyclicity of sliding cycles for regularized piecewise smooth visible-invisible two-folds, in the presence of singularities of the Filippov sliding vector field located away from two-folds. We obtain a slow-fast system after cylindrical blow-up and use a well-known connection between the divergence integral along orbits and transition maps for vector fields. Since properties of the divergence integral depend on the location and multiplicity of singularities, we divide the sliding cycles into different classes, which can then produce different types of cyclicity results. As an example, we apply our results to regularized piecewise linear systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_10409 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclicity of sliding cycles with singularities of regularized piecewise smooth visible-invisible two-folds Huang, Jicai Huzak, Renato Perez, Otavio Henrique Yao, Jinhui Dynamical Systems In this paper we study the cyclicity of sliding cycles for regularized piecewise smooth visible-invisible two-folds, in the presence of singularities of the Filippov sliding vector field located away from two-folds. We obtain a slow-fast system after cylindrical blow-up and use a well-known connection between the divergence integral along orbits and transition maps for vector fields. Since properties of the divergence integral depend on the location and multiplicity of singularities, we divide the sliding cycles into different classes, which can then produce different types of cyclicity results. As an example, we apply our results to regularized piecewise linear systems. |
| title | Cyclicity of sliding cycles with singularities of regularized piecewise smooth visible-invisible two-folds |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2503.10409 |