Total disconnectedness of Julia sets and absence of invariant linefields for real polynomials

Genadi Levin*, Sebastian Van Strien

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

In this paper we shall consider real polynomials with one (possibly degenerate) non-escaping critical (folding) point. Necessary and sufficient conditions are given for the total disconnectedness of the Julia set of such polynomials. Also we prove that the Julia sets of such polynomials do not carry invariant linefields. In the real case, this generalises the results by Branner and Hubbard for cubic polynomials and by McMullen on absence of invariant linefields.

Original languageAmerican English
Pages (from-to)161-172
Number of pages12
JournalAsterisque
Volume261
StatePublished - 2000

Keywords

  • Complex bounds
  • Julia sets
  • Local connectivity
  • Total disconnectedness

Fingerprint

Dive into the research topics of 'Total disconnectedness of Julia sets and absence of invariant linefields for real polynomials'. Together they form a unique fingerprint.

Cite this