Around 2011, Thurston considered the set of Galois conjugates of all entropies of superattracting real quadratic polynomials and produced pictures showing that its closure has a rich fractal structure. In this paper, we investigate the geometry of this set, which we call the entropy spectrum, relate it to the set of zeros of polynomials with restricted coefficients, and prove that it is path-connected and locally connected.
Galois Conjugates of Entropies of Real Unimodal Maps / Tiozzo, G.. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2020:2(2020), pp. 607-640. [10.1093/imrn/rny046]
Galois Conjugates of Entropies of Real Unimodal Maps
Tiozzo G.
2020
Abstract
Around 2011, Thurston considered the set of Galois conjugates of all entropies of superattracting real quadratic polynomials and produced pictures showing that its closure has a rich fractal structure. In this paper, we investigate the geometry of this set, which we call the entropy spectrum, relate it to the set of zeros of polynomials with restricted coefficients, and prove that it is path-connected and locally connected.File allegati a questo prodotto
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