No hyperbolic sets in J ∞ for infinitely renormalizable quadratic polynomials

Genadi Levin; Feliks Przytycki

doi:10.1007/s11856-022-2443-y

No hyperbolic sets in J _∞ for infinitely renormalizable quadratic polynomials

Genadi Levin^*, Feliks Przytycki

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let f be an infinitely renormalizable quadratic polynomial and J_∞ be the intersection of forward orbits of “small” Julia sets of its simple renormalizations. We prove that J_∞ contains no hyperbolic sets.

Original language	English
Pages (from-to)	635-656
Number of pages	22
Journal	Israel Journal of Mathematics
Volume	251
Issue number	2
DOIs	https://doi.org/10.1007/s11856-022-2443-y
State	Published - Dec 2022

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© 2022, The Hebrew University of Jerusalem.

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abstract = "Let f be an infinitely renormalizable quadratic polynomial and J∞ be the intersection of forward orbits of “small” Julia sets of its simple renormalizations. We prove that J∞ contains no hyperbolic sets.",

author = "Genadi Levin and Feliks Przytycki",

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year = "2022",

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doi = "10.1007/s11856-022-2443-y",

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AU - Przytycki, Feliks

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N2 - Let f be an infinitely renormalizable quadratic polynomial and J∞ be the intersection of forward orbits of “small” Julia sets of its simple renormalizations. We prove that J∞ contains no hyperbolic sets.

AB - Let f be an infinitely renormalizable quadratic polynomial and J∞ be the intersection of forward orbits of “small” Julia sets of its simple renormalizations. We prove that J∞ contains no hyperbolic sets.

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No hyperbolic sets in J _∞ for infinitely renormalizable quadratic polynomials

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