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Bibliographic Details
Main Authors: Lima, Maurício Firmino Silva, Perdigão, Tiago Rodrigo
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2407.02782
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Table of 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.