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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DOI : 10.5802/cml.15
Classification : 34H99, 58J35, 60H99
Bailleul, Ismaël 1

1 IRMAR, 263 Avenue du General Leclerc, 35042 RENNES, France
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Bailleul, Ismaël. Regularity of the Itô-Lyons map. Confluentes Mathematici, Tome 7 (2015) no. 1, pp. 3-11. doi : 10.5802/cml.15. http://www.numdam.org/articles/10.5802/cml.15/

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