Composants and the structure of periodic orbits for interval maps

Suppose f is a map from an interval [ a , b ] into itself with a periodic orbit consisting of the points p 1 < p 2 < ⋯ < p n . This paper begins with an analysis of the structure of periodic orbits for interval maps. Blocks are defined and used to describe this structure. With these structural theorems in place, results relating blocks of p 1 , p 2 , … , p n to irreducibility in the inverse limit of { [ a , b ] , f } are proved. ng p 1 , p 2 , … , p n is a Markov partition for f, necessary and sufficient conditions are given for two points of the inverse limit to belong to the same composant. This characterization of composants is used to show that the inverse limit is an E 0 -type continuum.