5 problems

Generic unbounded-distortion conjecture. For every non-Dini-integrable $\omega\in K$, unbounded distortion is $C^1$-generic in $\Gamma_{\omega}^{1}(\mathbb S^1)$.

Minimizing upper-Lyapunov measure conjecture. For a generic expanding self-map $T$ on a manifold $M$, the minimizing measure of the upper Lyapunov exponent $\lambda_1$ exists, is u…

Upper Lyapunov exponent maximizing-measure conjecture. If $k\geq 2$, then for a $C^k$-generic expanding self-map $T$, the upper Lyapunov exponent has a unique maximizing measure, s…

Jenkinson–Morris conjecture. For a generic $T\in\mathcal{E}^k$, the Lyapunov minimizing measure is unique and supported on a periodic orbit of $T$.

Let $f$ be a two-branch expanding map, and let $L$ denote its Lyapunov spectrum. Iommi–Kiwi conjecture. The Lyapunov spectrum $L$ has at most two points of inflection. This conject…