A P ] 2 0 O ct 2 00 6 CONSTRUCTION OF A GIBBS MEASURE ASSOCIATED TO THE PERIODIC BENJAMIN-ONO EQUATION

@inproceedings{Tzvetkov2006AP,
  title={A P ] 2 0 O ct 2 00 6 CONSTRUCTION OF A GIBBS MEASURE ASSOCIATED TO THE PERIODIC BENJAMIN-ONO EQUATION},
  author={Nikolay Tzvetkov},
  year={2006}
}
We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the ODE’s which correspond to the projection of the Benjamin-Ono equation, posed on the circle, on the first N , N ≥ 1 modes in the trigonometric bases. 

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