# On the set of periodic intervals of an interval map

*2010, Volume 15, Numbers 2-3, pp. 378-381*

Author(s):

**Matviichuk M.**

We investigate the closure of the set of periodic closed intervals for a continuous interval map with respect to Hausdorff metric. We prove that if a nondegenerate interval is limit of periodic ones then either a) it is periodic itself, or b) it is asymptotically degenerate, i.e. its diameter tends to 0 (when iterating under $f$). We present a continuous interval map for which case b) is possible.

Access to the full text on the Springer website |