7 problems

Let $\mathcal{B}_1'$ be the space in which the linearized renormalization dynamics is considered, let $L_1$ be the map given by the referenced equation, and let…

Let ${\mathcal S}_{{\mathcal P}}$ be a wild solenoid, meaning a weak solenoid with the wild asymptotic discriminant behavior constructed in the paper. A non-embedding conjecture fo…

Let $S(\Lambda,\vec{p})$ be the solenoid under consideration, with first-coordinate projection $\vec{x}\mapsto x_1$ into $\Sigma$, and let $NG$ be the set of points of $\Sigma$ tha…

Conjecture. If a weak solenoid admits an embedding in a $C^2$-foliation, then it is a normal solenoid with nilpotent covering groups.

Knotted-embedding conjecture. If a solenoid is embedded in two “different” knotted ways, the fundamental groups of the complements are different:

Unknotted-embedding conjecture. For every solenoid, there are uncountably many inequivalent unknotted embeddings in $S^3$.

Let $N$ be the dilation parameter, let ${\mathcal S}_N$ be the associated solenoid with measure $\tau$, and let the winding line be the image of the embedding of $\mathbb R$ into…