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Optimal periodic orbits for non-recurrent rational functions

Urbański M.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 2

175-184

We prove that each non-parabolic periodic orbit contained in the omega-limit set of a measure-recurrent, optimal orbit for a continuous function defined on the Julia set of a non-recurrent rational function is also optimal. As a by-product, we prove in the next section appropriate versions of shadowing and closing lemmas for non-recurrent rational functions.