Topologies for geometric flows and continuous dependence on parameters

Andrew D. Lewis; Yanlei Zhang

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arXiv · 2310.12293

Topologies for geometric flows and continuous dependence on parameters

Andrew D. Lewis·Yanlei Zhang

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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.

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Andrew D. Lewis, Yanlei Zhang. 2023-10-18. Topologies for geometric flows and continuous dependence on parameters. https://arxiv.org/abs/2310.12293

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