Dans ce document, we prove that there exists a residual subset of contact forms
$\lambda$ (if any) on a compact orientable manifold $M$ for which the foliation
de Rham cohomology of the associated Reeb foliation
$F_\lambda$ is trivial in that both $H^0(F_\lambda,{\mathbb R})$ et
$H^1(F_\lambda,{\mathbb R})$ are isomorphic to $\mathbb R$. For any choice of
$\lambda$ from the aforementioned residual subset, this cohomological result
can be restated as any of the following two equivalent statements: (1) The
functional equation $R_{\lambda}[f] = u$ is \emph{uniquely} solvable (modulo
the addition by constant)
for any $u$ satisfying $\int_M u\, d\mu_\lambda =0$, ou (2) The Lie algebra
of the group of strict contactomorphisms is isomorphic to the span of Reeb
vector fields, and so isomorphic to the 1 dimensional abelian Lie algebra
$\mathbb R$.
This result is also a key ingredient for the proof of the generic scarcity
result of strict contactomorphisms by Savelyev and the author.

Cet article explore les excursions dans le temps et leurs implications.

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