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|Title:||Parapuzzle of the multibrot set and typical dynamics of unimodal maps||Authors:||Avila, A.
|Issue Date:||2011||Citation:||Avila, A., Lyubich, M., Shen, W. (2011). Parapuzzle of the multibrot set and typical dynamics of unimodal maps. Journal of the European Mathematical Society 13 (1) : 27-56. ScholarBank@NUS Repository. https://doi.org/10.4171/JEMS/243||Abstract:||We study the parameter space of unicritical polynomials fc: z zd + c. For complex parameters, we prove that for Lebesgue almost every c, the map fc is either hyperbolic or infinitely renormalizable. For real parameters, we prove that for Lebesgue almost every c, the map fc is either hyperbolic, or Collet-Eckmann, or infinitely renormalizable. These results are based on controlling the spacing between consecutive elements in the "principal nest" of parapuzzle pieces. © European Mathematical Society 2011.||Source Title:||Journal of the European Mathematical Society||URI:||http://scholarbank.nus.edu.sg/handle/10635/103915||ISSN:||14359855||DOI:||10.4171/JEMS/243|
|Appears in Collections:||Staff Publications|
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