3 problems

Prevalent singularity spectrum conjecture. For every $f\in\widetilde{b}^{\mu,\Psi}_{p,q}([0,1]^d)$,

Prevalence conjecture. Almost every UDV map, in the sense of prevalence, is multi-chaotic.

Let $D=d+d'$ and let $B^{s}_{p,q}(\mathbb{R}^D)$ be the Besov space under the hypotheses on $p,q,s$ of Theorem. For a $d$-dimensional subspace $\mathcal{H}$ of $\mathbb{R}^D$, writ…