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A Homological Approach to Dynamics
Abstract
This note describes a novel approach to systematically characterize dynamics based on finite information. We present an algebraic framework for dynamics from which it is possible to deduce more traditional descriptors associated with the qualitative structures of the geometric theory of dynamical systems. The purpose of this paper is to indicate how this approach can be used to obtain interpretable characterizations of dynamics that are robust with respect to perturbations, in the context of models of multiscale and data-driven systems.
Related
BibTeX
@misc{kalies2026homological,
title = {{A Homological Approach to Dynamics}},
author = {William Kalies and Konstantin Mischaikow and Robert Vandervorst},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36532},
eprint = {2610.36532},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36532},
}
RIS
TY - UNPB
TI - A Homological Approach to Dynamics
AU - William Kalies
AU - Konstantin Mischaikow
AU - Robert Vandervorst
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36532
UR - https://arxiv.org/abs/2610.36532
AB - This note describes a novel approach to systematically characterize dynamics based on finite information. We present an algebraic framework for dynamics from which it is possible to deduce more traditional descriptors associated with the qualitative structures of the geometric theory of dynamical systems. The purpose of this paper is to indicate how this approach can be used to obtain interpretable characterizations of dynamics that are robust with respect to perturbations, in the context of models of multiscale and data-driven systems.
ER -