Geodesic
Ito equation as a geodesic flow on $\widehat {\text{Diff}\sp {s}(S\sp 1) \bigodot C\sp {\infty }(S\sp 1)}$
Archivum mathematicum, Tome 36 (2000) no. 4, pp. 305-312 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 35Q53, 37K10, 37K65, 58D05
Keywords: Bott-Virasoro Group; Ito equation 
@article{ARM_2000_36_4_a7,
     author = {Guha, Partha},
     title = {Ito equation as a geodesic flow on $\widehat {\text{Diff}\sp {s}(S\sp 1) \bigodot C\sp {\infty }(S\sp 1)}$},
     journal = {Archivum mathematicum},
     pages = {305--312},
     year = {2000},
     volume = {36},
     number = {4},
     mrnumber = {1811175},
     zbl = {1049.37045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2000_36_4_a7/}
}
TY  - JOUR
AU  - Guha, Partha
TI  - Ito equation as a geodesic flow on $\widehat {\text{Diff}\sp {s}(S\sp 1) \bigodot C\sp {\infty }(S\sp 1)}$
JO  - Archivum mathematicum
PY  - 2000
SP  - 305
EP  - 312
VL  - 36
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ARM_2000_36_4_a7/
LA  - en
ID  - ARM_2000_36_4_a7
ER  - 
%0 Journal Article
%A Guha, Partha
%T Ito equation as a geodesic flow on $\widehat {\text{Diff}\sp {s}(S\sp 1) \bigodot C\sp {\infty }(S\sp 1)}$
%J Archivum mathematicum
%D 2000
%P 305-312
%V 36
%N 4
%U http://geodesic.mathdoc.fr/item/ARM_2000_36_4_a7/
%G en
%F ARM_2000_36_4_a7
Guha, Partha. Ito equation as a geodesic flow on $\widehat {\text{Diff}\sp {s}(S\sp 1) \bigodot C\sp {\infty }(S\sp 1)}$. Archivum mathematicum, Tome 36 (2000) no. 4, pp. 305-312. http://geodesic.mathdoc.fr/item/ARM_2000_36_4_a7/