5 problems

Local-manifold conjecture. The assumption $\operatorname{D}G(0)=\operatorname{D}^2G(0)=0$ can be removed while still obtaining local rough invariant manifolds.

Let $F:\mathcal{X}\to\mathcal{X}$ satisfy $F(0)={\textnormal{D}}F(0)=0$, and let $G:\mathcal{X}\to\mathcal{L}(\mathcal{V},\mathcal{X})$ satisfy the regularity and Lipschitz conditi…

Let $H\in(0,1)$ be the Hurst parameter of fractional Brownian motion, and let $\gamma$ denote the Hölder regularity exponent of the coefficient $\sigma$. Pathwise uniqueness failur…

Let $H\in[1,\infty)\setminus\mathbb{N}$ be the Hurst parameter of fractional Brownian motion, and let $\gamma$ denote the Hölder regularity exponent of the coefficient $\sigma$. Th…

One-dimensional driving-signal conjecture. Uniqueness should hold for any one-dimensional driving signal; equivalently, assertion $\textbf{(A)}_{d,1,p}$ should hold for arbitrary…