Dynamical Systems On Generalised Klein Bottles
Dynamical Systems
2024-12-18 v2 General Topology
Abstract
We propose a high dimensional generalisation of the standard Klein bottle, going beyond those considered previously. We address the problem of generating continuous scalar fields (distributions) and dynamical systems (flows) on such state spaces, which can provide a rich source of examples for future investigations. We consider a class of high dimensional dynamical systems that model distributed information processing within the human cortex, which may be capable of exhibiting some Klein bottle symmetries. We deploy topological data analytic methods in order to analyse their resulting dynamical behaviour, and suggesting future challenges.
Cite
@article{arxiv.2411.06215,
title = {Dynamical Systems On Generalised Klein Bottles},
author = {Peter Grindrod and Ka Man Yim},
journal= {arXiv preprint arXiv:2411.06215},
year = {2024}
}