Braids and linked periodic orbits of disc homeomorphisms

This paper concerns on linked periodic orbits of orientation-preserving homeomorphisms of the $2$-disc in the sense of Gambaudo. We interpret the linking of periodic orbits by using their induced braids. Then based on the forcing relation of braids, we present a method for finding periodic orbits which are linked with a given one. In particular, for $3$-periodic orbits of pseudo-Anosov braid types, we provide new examples of linked orbits of periods at most $4$.