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Communications in Mathematical Physics

, Volume 341, Issue 3, pp 733–749 | Cite as

Quadratic-Like Dynamics of Cubic Polynomials

  • Alexander Blokh
  • Lex Oversteegen
  • Ross Ptacek
  • Vladlen Timorin
Article

Abstract

A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.

Keywords

Periodic Point Stable Component Parabolic Point Siegel Disk Holomorphic Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Alexander Blokh
    • 1
  • Lex Oversteegen
    • 1
  • Ross Ptacek
    • 1
  • Vladlen Timorin
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA
  2. 2.Faculty of MathematicsNational Research University Higher School of EconomicsMoscowRussia
  3. 3.Independent University of MoscowMoscowRussia

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