Computing the exact number of periodic orbits for planar flows
Dynamical Systems
2022-11-01 v2 Logic in Computer Science
Logic
Abstract
In this paper, we consider the problem of determining the \emph{exact} number of periodic orbits for polynomial planar flows. This problem is a variant of Hilbert's 16th problem. Using a natural definition of computability, we show that the problem is noncomputable on the one hand and, on the other hand, computable uniformly on the set of all structurally stable systems defined on the unit disk. We also prove that there is a family of polynomial planar systems which does not have a computable sharp upper bound on the number of its periodic orbits.
Cite
@article{arxiv.2101.07701,
title = {Computing the exact number of periodic orbits for planar flows},
author = {Daniel S. Graça and Ning Zhong},
journal= {arXiv preprint arXiv:2101.07701},
year = {2022}
}