J. Guaschi, REPRESENTATIONS OF ARTINS BRAID-GROUPS AND LINKING NUMBERS OF PERIODIC-ORBITS, Journal of knot theory and its ramifications, 4(2), 1995, pp. 197-212
Let P be a periodic orbit of period n greater than or equal to 3 of an
orientation-preserving homeomorphism f of the 2-disc. Let q be the le
ast integer greater than or equal to n/2 - 1. Then f admits a periodic
orbit and of period less than or equal to q such that the linking num
ber of P about Q is non-zero. This answers a question of Franks in the
affirmative in the case that P has small period. We also derive a res
ult regarding matrix representations of Artin's braid groups. Finally
a lower bound for the topological entropy of a braid in terms of the t
race of its Burau matrix is found.