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Two counterexamples in rational and interval dynamics

Abstract

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 [12] 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.
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hal-00796888 , version 1 (05-03-2013)

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  • HAL Id : hal-00796888 , version 1

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Nicolae Mihalache. Two counterexamples in rational and interval dynamics. 2009. ⟨hal-00796888⟩
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