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


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.


Periodic Point Stable Component Parabolic Point Siegel Disk Holomorphic Motion 
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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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