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Currently displaying 1 – 7 of 7

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A note on bidifferential calculi and bihamiltonian systems

Partha Guha — 2004

Archivum Mathematicum

In this note we discuss the geometrical relationship between bi-Hamiltonian systems and bi-differential calculi, introduced by Dimakis and Möller–Hoissen.

Ito equation as a geodesic flow on $\hat{{Diff}^{s} (S^{1}) ⨀ C^{\infty} (S^{1})}$

Partha Guha — 2000

Archivum Mathematicum

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