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Langues de Arnold de la famille standard double Explosion de cycle dans la famille quadratique

Abstract : The connectedness of the tongues of the double standard map family is shown by quasiconformal deformation. I determine the growth rate of the coefficient of the Laurent series of inverse of the Böttcher map for quadratic polynomials with escaping critical point. An inequality that yields a domain on which there is no critical value of the multiplier map is derived from the theory of quadratic differentials. I give an alternate proof of Levin criterium for non local connectedness of infinite satellite renormalizable quadratic Julia sets. A geometric model of this situation is also investigated.
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https://theses.hal.science/tel-00666001
Contributor : Alexandre De Zotti Connect in order to contact the contributor
Submitted on : Friday, February 3, 2012 - 1:00:46 PM
Last modification on : Tuesday, October 25, 2022 - 11:58:10 AM
Long-term archiving on: : Friday, May 4, 2012 - 2:40:38 AM

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  • HAL Id : tel-00666001, version 1

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Alexandre Dezotti. Langues de Arnold de la famille standard double Explosion de cycle dans la famille quadratique. Systèmes dynamiques [math.DS]. Université Paul Sabatier - Toulouse III, 2011. Français. ⟨NNT : ⟩. ⟨tel-00666001⟩

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