Endomorphisms of the Lie algebroids up to homotopy.
In 2001, B. Malgrange defines the D-envelope or galoisian envelope of an analytical dynamical system. Roughly speaking, this is the algebraic hull of the dynamical system. In this short article, the D-envelope of a rational map R: P1 --> P1 is computed. The rational maps characterised by a finitness property of their D-envelope appear to be the integrable ones.
We prove that on an asymptotically Euclidean boundary groupoid, the heat kernel of the Laplacian is a smooth groupoid pseudo-differential operator.