# When is the unit ball in $\text{Ham}(M,\omega)$ with respect to the Hofer metric contractible?

Associated to a symplectic manifold $$(M^{2n},\omega)$$ is the group of (compactly supported) Hamiltonian diffeomorphisms $$\text{Ham}(M,\omega)$$. This group is equipped with the famous Hofer metric $$d_H$$. Denote by $$\mathcal{B}$$ the unit ball in $$\text{Ham}(M,\omega)$$ with respect to $$d_H$$. Are any examples known where $$\mathcal{B}$$ is contractible? Are examples known where $$\mathcal{B}$$ is not contractible?

I know that it is known in some cases if $$\text{Ham}(M,\omega)$$ is contractible or not (See e.g. McDuff's "A survey of the topological properties of symplectomorphism groups"). My question is closer to the following idea: If a loop $$\mathcal{B}$$ is contractible, can a contracting disc then be realized inside $$\mathcal{B}$$?