On James Hyde's example of non-orderable subgroup of \(\text{Homeo}(D,\partial D)\) (Q2070052)

Summary: In [Ann. Math. (2) 190, No. 2, 657--661 (2019; Zbl 07107184)] \textit{J. Hyde} presented the first example of non-left-orderable, finitely generated subgroup of \(\text{Homeo}(D,\partial D)\), the group of homeomorphisms of the disk fixing the boundary. This implies that the group \(\text{Homeo}(D,\partial D)\) itself is not left-orderable. We revisit the construction, and present a slightly different proof of purely dynamical flavor, avoiding direct references to properties of left-orders. Our approach allows to solve the analogue problem for actions on the circle.