8 problems

Let $T$ be a trellis and let $f$ be a trellis map for $T$. Write $N_\infty(f)$ for the asymptotic Nielsen number and $h_\mathit{top}$ for topological entropy. Optimality conjecture…

General Floer homology and asymptotic growth conjecture.

Bounded convex decomposition conjecture. There exists a map

Bounded-deviation strengthening. There exists $C>0$ such that if an orbit $\widetilde y,\dots,\widetilde f^{n_0}(\widetilde y)$ of $\widetilde f$ crosses $V_C(\widetilde\gamma)$ fo…

Exact minimal stretch factor conjecture. The normalized stretch factor of $f$ is greater than or equal to the largest real root of

Let $\phi$ be a pA mutation loop on a marked surface $\Sigma$. Write $\mathcal{E}_\phi^a$ for its associated asymptotic entropy and $\lambda_{\pi(\phi)}$ for the spectral radius of…

Tresser's conjecture. Generically, maps in the boundary of positive topological entropy have a set of periodic orbits which, except for a finite subset, consists of infinitely many…

Let $S_g$ be a closed orientable surface, let $f\in\operatorname{Mod}(S_g)$ be pseudo-Anosov with stretch factor $\lambda$, and let $C$ be the constant appearing in the small-stret…