Topologies for geometric flows and continuous dependence on parameters
Autor: | Lewis, Andrew D., Zhang, Yanlei |
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Rok vydání: | 2023 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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. Comment: arXiv admin note: substantial text overlap with arXiv:2202.00741 |
Databáze: | arXiv |
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