Two counterexamples in rational and interval dynamics

Details Two counterexamples in rational and interval dynamics Two counterexamples in rational and interval dynamics

2008-10-08

arxiv.org/abs/0810.1474v1

Mathematics

Dynamical Systems

49 pages, 2 figures

Scientific paper

In rational dynamics, we prove the existence of a polynomial that satisfies the Topological Collet-Eckmann condition, but which has a recurrent critical orbit that is not Collet-Eckmann. This shows that the converse of the main theorem in [11] does not hold. In interval dynamics, we show that the Collet-Eckmann property for recurrent critical orbits is not a topological invariant for real polynomials with negative Schwarzian derivative. This contradicts a conjecture of Swiatek [22].

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