Let pi and theta be cyclic permutations of finite ordered sets. We say that pi forces theta if every continuous map of the interval which has a representative of pi also has one of theta . We give a geometric version of Jungreis' combinatorial algorithm for deciding in certain cases whether pi forces theta .
Transactions of the American Mathematical Society
Bernhardt, Chris; Coven, E.; Misiurewicz, M.; and Mulvey, Irene, "Comparing Periodic Orbits of Maps of the Interval" (1992). Math & Computer Science Faculty Publications. 4.
C. Bernhardt, E. Coven, M. Misiurewicz, and I. Mulvey. Comparing Periodic Orbits of Maps of the Interval, Transactions of the American Mathematical Society. 333(2), 701-707.