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

Partha Guha

Archivum Mathematicum (2000)

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

Abstract

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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.

How to cite

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Guha, 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 -

References

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