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arXiv · 2407.02782

One-dimensional Piecewise Smooth Rational Degree Maps

Maurício Firmino Silva Lima·Tiago Rodrigo Perdigão
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Abstract

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 $\Sigma$ 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 $\Sigma$ 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.

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Maurício Firmino Silva Lima, Tiago Rodrigo Perdigão. 2024-07-03. One-dimensional Piecewise Smooth Rational Degree Maps. https://arxiv.org/abs/2407.02782

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