One-dimensional Piecewise Smooth Rational Degree Maps

2024/07/03 by Maurício Firmino Silva Lima, Lima, Maurício Firmino Silva, Tiago Rodrigo Perdigão +1
Engineering · Computer Science · #Advanced Numerical Analysis Techniques #Advanced Vision and Imaging #Computational Geometry and Mesh Generation

paper · pdf · doi:10.48550/arxiv.2407.02782

Abstract

In this paper, we consider a class of continuous maps characterized by a singularity of order x^q/p (with p,q ∈ 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.

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