Recent advances in rigorous computation of Poincar\'e maps
Tomasz Kapela, Daniel Wilczak, Piotr Zgliczy\'nski
TL;DR
This paper reviews recent interval-based methods for rigorously computing Poincaré maps, emphasizing how the choice of sections and coordinates affects the accuracy of bounds near fixed points.
Contribution
It introduces recent advances in interval methods for Poincaré map computation and analyzes the influence of section and coordinate choices on bounds.
Findings
Interval methods improve rigor in Poincaré map computation
Section and coordinate choices significantly impact bounds accuracy
Recent techniques enhance fixed point analysis
Abstract
In this article we present recent advances on interval methods for rigorous computation of Poincar\'e maps. We also discuss the impact of choice of Poincar\'e section and coordinate system on obtained bounds for computing Poincar\'e map nearby fixed points.
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