Regularity of the Itô-Lyons map
Confluentes Mathematici, Tome 7 (2015) no. 1, pp. 3-11.

We show in this note that the Itô-Lyons solution map associated to a rough differential equation is Fréchet differentiable when understood as a map between some Banach spaces of controlled paths. This regularity result provides an elementary approach to Taylor-like expansions of Inahama-Kawabi type for solutions of rough differential equations depending on a small parameter, and makes the construction of some natural dynamics on the path space over any compact Riemannian manifold straightforward, giving back Driver’s flow as a particular case.

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Classification : 34H99,  58J35,  60H99
     author = {Isma\"el Bailleul},
     title = {Regularity of the {It\^o-Lyons} map},
     journal = {Confluentes Mathematici},
     pages = {3--11},
     publisher = {Institut Camille Jordan},
     volume = {7},
     number = {1},
     year = {2015},
     doi = {10.5802/cml.15},
     language = {en},
     url = {}
Ismaël Bailleul. Regularity of the Itô-Lyons map. Confluentes Mathematici, Tome 7 (2015) no. 1, pp. 3-11. doi : 10.5802/cml.15.

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