ITO EQUATION AS A GEODESIC FLOW ON $\pmb{\widehat{Diff^s(S^1) \bigodot C^{\infty}(S^1)}}$

Partha Guha

Address. S.N. Bose National Centre for Basic Sciences, JD Block, Sector-3, Salt Lake, Calcutta-700091, INDIA


Abstract. The Ito equation is shown to be a geodesic flow of $L^2$ metric on the semidirect product space ${\widehat {Diff^s(S^1) \bigodot C^{\infty}(S^1)}}$, 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.

AMSclassification. 58D05, Secondary 35Q53

Keywords. Bott-Virasoro Group, Ito equation