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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.02782 |
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| _version_ | 1866917711868592128 |
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| author | Lima, Maurício Firmino Silva Perdigão, Tiago Rodrigo |
| author_facet | Lima, Maurício Firmino Silva Perdigão, Tiago Rodrigo |
| contents | In this paper, we consider a class of continuous maps characterized by a singularity of order $x^{q/p}$ (with $p,q \in \mathbb{N}$, $p>q$, and $(p,q)=1$) on one side of the discontinuity boundary $Σ$ and a linear behaviour on the other side. Such maps arise naturally in the study of grazing bifurcations of hybrid and piecewise flows. In this context the boundary collision of a fixed point of the map with $Σ$ then corresponds to a grazing bifurcation of the flow. We will start by studying one-dimensional maps, and the main result of this paper is a classification of all bifurcation scenarios, including: period doubling and robust chaos. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02782 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One-dimensional Piecewise Smooth Rational Degree Maps Lima, Maurício Firmino Silva Perdigão, Tiago Rodrigo Dynamical Systems In this paper, we consider a class of continuous maps characterized by a singularity of order $x^{q/p}$ (with $p,q \in \mathbb{N}$, $p>q$, and $(p,q)=1$) on one side of the discontinuity boundary $Σ$ and a linear behaviour on the other side. Such maps arise naturally in the study of grazing bifurcations of hybrid and piecewise flows. In this context the boundary collision of a fixed point of the map with $Σ$ then corresponds to a grazing bifurcation of the flow. We will start by studying one-dimensional maps, and the main result of this paper is a classification of all bifurcation scenarios, including: period doubling and robust chaos. |
| title | One-dimensional Piecewise Smooth Rational Degree Maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2407.02782 |