ESCAPE DYNAMICS FOR INTERVAL MAPS

We study the structure of the escape orbits for a certain class of interval maps. This structure is encoded in the escape transition matrix (A) over cap (f) of an interval map f, extending the traditional matrix A(f) which considers the transition among the Markov subintervals. We show that the escape transition matrix is a topological conjugacy invariant. We then characterize the 0-1 matrices that can be fabricated as escape transition matrices of Markov interval maps f with escape sets. This shows the richness of this class of interval maps.