# Ito equation as a geodesic flow on $\widehat{{\text{Diff}}^{s}\left({S}^{1}\right)\u2a00{C}^{\infty}\left({S}^{1}\right)}$

Archivum Mathematicum (2000)

- Volume: 036, Issue: 4, page 305-312
- ISSN: 0044-8753

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topGuha, Partha. "Ito equation as a geodesic flow on $\widehat{\text{Diff}^{s}(S^1) \bigodot C^{\infty }(S^1)}$." Archivum Mathematicum 036.4 (2000): 305-312. <http://eudml.org/doc/248576>.

@article{Guha2000,

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

author = {Guha, Partha},

journal = {Archivum Mathematicum},

keywords = {Bott-Virasoro Group; Ito equation; Bott-Virasoro group; Ito equation},

language = {eng},

number = {4},

pages = {305-312},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Ito equation as a geodesic flow on $\widehat\{\text\{Diff\}^\{s\}(S^1) \bigodot C^\{\infty \}(S^1)\}$},

url = {http://eudml.org/doc/248576},

volume = {036},

year = {2000},

}

TY - JOUR

AU - Guha, Partha

TI - Ito equation as a geodesic flow on $\widehat{\text{Diff}^{s}(S^1) \bigodot C^{\infty }(S^1)}$

JO - Archivum Mathematicum

PY - 2000

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 036

IS - 4

SP - 305

EP - 312

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

LA - eng

KW - Bott-Virasoro Group; Ito equation; Bott-Virasoro group; Ito equation

UR - http://eudml.org/doc/248576

ER -

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