Accessible points in the Julia sets of stable exponentials

Ranjit Bhattacharjee, Robert L. Devaney, Lee DeVille, Kresimir Josi, Monica Moreno-Rocha

Research output: Contribution to journalArticlepeer-review


In this paper we consider the question of accessibility of points in the Julia sets of complex exponential functions in the case where the exponential admits an attracting cycle. In the case of an attracting fixed point it is known that the Julia set is a Cantor bouquet and that the only points accessible from the basin are the endpoints of the bouquet. In case the cycle has period two or greater, there are many more restrictions on which points in the Julia set are accessible. In this paper we give precise conditions for a point to be accessible in the periodic point case in terms of the kneading sequence for the cycle.

Original languageEnglish (US)
Pages (from-to)299-318
Number of pages20
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number3
StatePublished - 2001
Externally publishedYes


  • Accessibility
  • Cantor bouquets
  • Julia sets

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics


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