3 problems

Let a contact sub-connection have a control admissible symmetry group $G$ with $\dim G=1$. One-dimensional symmetry reduction conjecture. If the contact sub-connection is EDFL by p…

Let a contact sub-connection admit an ESFL reduction by a partial contact curve of codimension $s>1$. Codimension-one reduction conjecture. The contact sub-connection must also adm…

Let $X = X_0 + \sum X_i \circ \dfrac{dB_t^i}{dt}$ be an SDS on a manifold $M$. Suppose that $X$ is integrable and diffusion invariant with respect to an action of a compact Lie gro…