5 problems

Necessity conjecture. If the associated Markov chain is not ergodic of degree 2, then

Random Milnor attractor conjecture. Both relative attractors (or attracting regions) in the multiply degenerated subspaces $M_{wv}$ and the optimal attractors in…

Infinite-dimensional attractor conjecture. There are a nonlinearity $f$ and right-hand side $g$ satisfying those assumptions such that $$ mathcal A($eta) has infinite Hausdorff and…

Consider the two-dimensional stochastic differential equation exhibiting a Hopf bifurcation, with linear stability of the origin as the deterministic Hopf bifurcation parameter and…

Let $u0$ and let $rho$ be a weight whose definition involves a small constant $c0$. Consider the attractor in the deterministic case with no noise, $sigma=0$. Diameter conjecture.…