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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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https://hal-upec-upem.archives-ouvertes.fr/hal-00796888
Contributor : Nicolae Mihalache <>
Submitted on : Tuesday, March 5, 2013 - 11:21:48 AM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM
Long-term archiving on: : Thursday, June 6, 2013 - 3:56:49 AM

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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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