Doubling bifurcations of invariant closed curves in 3D maps
Dynamical Systems
2025-09-17 v1
Abstract
Numerous studies have reported two types of doubling of invariant closed curves (ICCs) in dynamical systems: (a) the creation of two disjoint ICCs such that iterations flip between them; and (b) the creation of a single ICC of double the length of the original ICC. Various methods have been proposed to analyze such bifurcations. We show that the methods proposed so far are not always adequate for analyzing and predicting these bifurcations. We propose a new method to overcome the difficulties.
Keywords
Cite
@article{arxiv.2509.12943,
title = {Doubling bifurcations of invariant closed curves in 3D maps},
author = {Sayanho Biswas and Soumitro Banerjee and Viktor Avrutin and Iryna Sushko},
journal= {arXiv preprint arXiv:2509.12943},
year = {2025}
}