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On critical renormalization of complex polynomials

Abstract : Holomorphic renormalization plays an important role in complex polynomial dynamics. We consider certain conditions guaranteeing that a polynomial which does not admit a polynomial-like connected Julia set still admits an invariant continuum on which it is topologically conjugate to a lower degree polynomial. This invariant continuum may contain extra critical points of the original polynomial that are not visible in the dynamical plane of the conjugate polynomial. Thus, we extend the notions of holomorphic renormalization and polynomial-like maps and describe a setup where new generalized versions of these notions are applicable and yield useful topological conjugacies.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03144538
Contributor : Peter Haïssinsky <>
Submitted on : Wednesday, February 17, 2021 - 4:45:38 PM
Last modification on : Thursday, February 18, 2021 - 3:28:20 AM

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  • HAL Id : hal-03144538, version 1
  • ARXIV : 2008.06689

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Alexander Blokh, Peter Haïssinsky, Lex Oversteegen, Vladlen Timorin. On critical renormalization of complex polynomials. 2021. ⟨hal-03144538⟩

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