14 problems

Linearizability conjecture. For $n\geq 3$, the equation is linearizable if and only if $F_y=0$; in that case, it is already a linear equation. The claim extends the verified analys…

Poisson linearization conjecture. If the restricted Lie algebroid $T^*_S M$ integrates to a compact, source 1-connected Lie algebroid, then $pi$ is linearizable around $S$.

Let a control system possess a control admissible symmetry group. EDFL-to-CFL conjecture. If the control system is EDFL, then it must be CFL. The conjecture concerns the relation b…

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 $p(z)$ denote the function associated with an ESFL reduction by a codimension $1$ partial contact curve, and let the truncated Euler operator and the higher-order Euler operato…

Let a control system with at least two controls be a Goursat bundle, and suppose it cannot be transformed to Brunovský normal form via an ESFT. DF linearization conjecture. The con…

Let $F_n=\mathbb{K}\langle x_1,\ldots,x_n\rangle$ be the free associative algebra, and let $\mathbb{T}_{n-1}$ be the $(n-1)$-dimensional algebraic torus. Free-associative torus-act…

For $n\geq 1$, let $P_n=\mathbb{K}[z_1,\ldots,z_{2n}]$ be the commutative Poisson algebra with bracket … An action is effective if its kernel is trivial, and regular if it is algeb…

Let $F_n$ be the free associative algebra on $n$ generators, and let $\mathbb{T}_{n-1}$ be the $(n-1)$-dimensional algebraic torus. An action is linearizable when it is conjugate t…

Let ${\rm SA}_n(\mathbb{K})$ denote the group of special polynomial automorphisms, and let ${\rm SLIN}_n(\mathbb{K})$ denote the corresponding subgroup satisfying the special linea…

Let $\mathbb{K}$ be a field, and let ${\rm GA}_n(\mathbb{K})$ denote the group of polynomial automorphisms of affine $n$-space over $\mathbb{K}$. Let ${\rm GLIN}_n(\mathbb{K})$ be…

Douady's conjecture. Polynomials and rational functions of degree $d\ge 2$ do not have exotic Siegel disks.

GLIN generation conjecture. If $\operatorname{char}(k)\ne2$, then