9 problems

Anti-involution conjecture. There are a neighborhood $U\ni m$ and an anti-involution $\alpha$ of the bihamiltonian structure on $U$ such that

Local classification conjecture. There is a local isomorphism of bihamiltonian structures between $M$ near $m$ and $\Phi(\cal W)$ near $m'$.

Let $M$ be a manifold with compatible Poisson structures $\{,\}_{1}$ and $\{,\}_{2}$. Let $L$ be a finite set with $r$ elements, and let $F_{l,\lambda}$, for $l\in L$ and…

Let $M$ and $M'$ carry homogeneous bihamiltonian structures … For small open subsets $U\subset M$ and $U'\subset M'$, let ${\cal B}_{U}$ and ${\cal B}_{U'}$ be the corresponding we…

The odd-dimensional open Volterra system, the even-dimensional periodic Volterra system, the full Toda lattice, the multidimensional Euler top, and the regular case of the cited bi…

Let $M_{1}$ and $M_{2}$ be manifolds equipped with bihamiltonian structures, and equip $M_{1}\times M_{2}$ with their product bihamiltonian structure. Product-flatness conjecture.…

Let a homogeneous bihamiltonian structure have type $\left(2k_{1}-1,2k_{2}-1,\dots,2k_{l}-1\right)$. Tensorial criterion for Kronecker structures. There exist $N>0$ and natural ten…

Consider the abstract local RH hierarchy and its hamiltonian perturbations possessing a $\tau$-structure; the abstract local Hodge mapping hierarchy is the hierarchy constructed fr…

Let a semisimple Frobenius manifold have an associated Principal Hierarchy, and let $(P_0,P_1)$ be a tau-symmetric bihamiltonian deformation of that hierarchy. The deformation has…