7 problems

Commutativity conjecture. The same conditions under which uniform-in-time averaging holds are sufficient to guarantee commutativity of the whole diagram.

Vanishing-anomaly conjecture. $H_{kq}$ vanishes.

Consider coarse-graining algorithms for dynamical systems, including methods based on weak formulations of the governing equations. Weak-form improvement conjecture. The weak form…

Consider the aliasing approach to coarse-graining, in which coarse sampling is used to recover reduced dynamics from a multiscale system. In the setting discussed, the test-functio…

Let $X_\varepsilon$ be a Hamiltonian vector field with approximate symmetries, and let higher-order averaged systems be obtained by the corresponding averaging and reduction proced…

The paper studies Markov chains on a finite state space, with coarse-grained dynamics obtained by grouping micro-states into macro-states. Discrete-time generalisation conjecture.…

In phase space, consider coarse graining with convex polyhedra in an $L_p$ sense, and a Hamiltonian system with many degrees of freedom whose collective behavior is being described…