Rays to renormalizations

• Autorzy: Levin Genadi

Identyfikatory

DOI

10.4064/ba210129-19-2

• Języki publikacji: EN

Abstrakty

EN

Let KP be the filled Julia set of a polynomial P, and K_f the filled Julia set of a renormalization f of P. We show, loosely speaking, that there is a finite-to-one function λ from the set of P-external rays having limit points in K_f onto the set of f-external rays to K_f such that R and λ(R) share the same limit set. In particular, if a point of the Julia set J_f = δK_f of a renormalization is accessible from C \ K_f then it is accessible through an external ray of P (the converse is obvious). Another interesting corollary is that a component of KP \ K_f can meet K_f only in a single (pre-)periodic point. We also study a correspondence induced by λ on arguments of rays. These results are generalizations to all polynomials (covering notably the case of connected Julia set K_p ) of some results of Levin and Przytycki (1996), Blokh et al. (2016) and Petersen and Zakeri (2019) where it is assumed that K_p is disconnected and K_f is a periodic component of K_p .

Słowa kluczowe

EN

Julia set; renormalization; external rays

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2020
• Tom: Vol. 68, no. 2
• Strony: 133--149
• Opis fizyczny: Biblogr. 19 poz.

Twórcy

autor

Levin Genadi

• Institute of Mathematics, The Hebrew University of Jerusalem Givat Ram, Jerusalem, 91904, Israel

Bibliografia

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• [Le12] G. Levin, Rays to renormalizations, manuscript, 2012.
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• [PZ19] C. Petersen and S. Zakeri, On the correspondence of external rays under renormalization, arXiv:1903.00800 (2019).
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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).