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Ito equation as a geodesic flow on Diff s ( S 1 ) C ( S 1 ) ^

Partha Guha (2000)

Archivum Mathematicum

The Ito equation is shown to be a geodesic flow of L 2 metric on the semidirect product space 𝐷𝑖𝑓𝑓 s ( S 1 ) C ( S 1 ) ^ , where 𝐷𝑖𝑓𝑓 s ( S 1 ) is the group of orientation preserving Sobolev H s diffeomorphisms of the circle. We also study a geodesic flow of a H 1 metric.

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