In the context of Synthetic Differential Geometry, we discuss vector fields/ordinary differential equations as actions; in particular, we exploit function space formation (exponential spaces) in the category of actions.
@article{bwmeta1.element.doi-10_1007_s11533-005-0005-2, author = {Anders Kock and Gonzalo Reyes}, title = {Ordinary differential equations and their exponentials}, journal = {Open Mathematics}, volume = {4}, year = {2006}, pages = {64-81}, zbl = {1105.51004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1007_s11533-005-0005-2} }
Anders Kock; Gonzalo Reyes. Ordinary differential equations and their exponentials. Open Mathematics, Tome 4 (2006) pp. 64-81. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1007_s11533-005-0005-2/
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