No hyperbolic sets in J_\infty for infinitely renormalizable quadratic polynomials
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Publication:6373733
DOI10.1007/S11856-022-2443-YarXiv2107.11962MaRDI QIDQ6373733
Feliks Przytycki, Genadi Levin
Publication date: 26 July 2021
Abstract: Let f be an infinitely-renormalizable quadratic polynomial and J_infty be the intersection of forward orbits of "small" Julia sets of simple renormalizations of f. We prove that J_infty contains no hyperbolic sets.
Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems (37F15) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Renormalization of holomorphic dynamical systems (37F25)
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