Location of Siegel capture polynomials in parameter spaces

Academic Article


  • A cubic polynomial with a marked fixed point 0 is called an IS-capture polynomial if it has a Siegel disk D around 0 and if D contains an eventual image of a critical point. We show that any IS-capture polynomial is on the boundary of a unique bounded hyperbolic component of the polynomial parameter space determined by the rational lamination of the map and relate IS-capture polynomials to the cubic principal hyperbolic domain and its closure.
  • Published In

  • Nonlinearity  Journal
  • Digital Object Identifier (doi)

    Author List

  • Blokh A; Ch'eritat A; Oversteegen L; Timorin V
  • Start Page

  • 2430
  • End Page

  • 2453
  • Volume

  • 34
  • Issue

  • 4