有理动力学和区间动力学中的两个反例
Two counterexamples in rational and interval dynamics
摘要：
在有理动力学中，我们证明了一个多项式的存在性，它满足拓扑Collet-Eckmann条件，但它有一个经常性的临界轨道是不是Collet-Eckmann。这表明[11]中主要定理的逆命题不成立。在区间动力学中，我们证明了对于具有负Schwarzian导数的实多项式，常返临界轨道的Collet-Eckmann性质不是拓扑不变量。这与Swiatek的猜想相矛盾[22]。
英文摘要：
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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