6 problems

Let $Y(10,10,\pi/2)$ be the funneled torus considered in the numerical study, with its Klein four-group of symmetries, and let invariant Ruelle distributions be computed using a cy…

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 $q,p\in\mathbb{R}^3$, and let $\mathrm{O}(3)$ act diagonally on $(q,p)$. Define the invariant coordinates … Suppose that $\bar H(q,p)$ is a smooth $\mathrm{O}(3)$-invariant fun…

Let $\boldsymbol{\omega}$ be the Pfaffian system … and let ${\mathcal{E}}=\ker\boldsymbol{\omega}$, describing the under-actuated ship system. Symmetry-group conjecture. The symmet…

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…