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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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Contributor : Nicolae Mihalache Connect in order to contact the contributor
Submitted on : Tuesday, March 5, 2013 - 11:21:48 AM
Last modification on : Saturday, January 15, 2022 - 4:09:16 AM
Long-term archiving on: : Thursday, June 6, 2013 - 3:56:49 AM


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  • HAL Id : hal-00796888, version 1


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



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