Japanese Journal of Mathematics

, Volume 3, Issue 1, pp 1–17

Invariant or quasi-invariant probability measures for infinite dimensional groups

Part I: Non-ergodicity of Euler hydrodynamic
Special Feature: The 3rd Takagi Lectures

DOI: 10.1007/s11537-008-0751-6

Cite this article as:
Malliavin, P. Jpn. J. Math. (2008) 3: 1. doi:10.1007/s11537-008-0751-6


Deterministic Euler flow on a torus cannot leave invariant any probability measure.

To the Japanese Mathematical Community, with my admiration and my warmest friendship.

Keywords and phrases

group of diffeomorphismsMalliavin calculusrandom unitary operatorexistence of Euler flow

Mathematics subject classification (2000)


Copyright information

© The Mathematical Society of Japan and Springer Japan 2008

Authors and Affiliations

  1. 1.ParisFrance