Topologies for geometric flows and continuous dependence on parameters
Geometric Topology
2023-10-20 v1
Abstract
We study time- and parameter-dependent ordinary differential equations in the geometric setting of vector fields and their flows. Various degrees of regularities in state are considered, including Lipschitz, finitely diferentiable, smooth, and holomorphic. A suitable topology for the space of flows is derived using geometric descriptions of suitable topologies for vector fields. A new kind of continuous dependence is proved, that of the fixed time local flow on the parameter in a general topological space.
Cite
@article{arxiv.2310.12293,
title = {Topologies for geometric flows and continuous dependence on parameters},
author = {Andrew D. Lewis and Yanlei Zhang},
journal= {arXiv preprint arXiv:2310.12293},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2202.00741