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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Accessible points in the Julia sets of stable exponentials

Pages: 299 - 318, Volume 1, Issue 3, August 2001

doi:10.3934/dcdsb.2001.1.299       Abstract        Full Text (358.9K)       Related Articles

Ranjit Bhattacharjee - Department of Mathematics and Statistics, Boston University, 111 Cumminton St., Boston, MA 02215, United States (email)
Robert L. Devaney - Department of Mathematics and Statistics, Boston University, 111 Cummington St., Boston, MA 02215, United States (email)
R.E. Lee Deville - Department of Mathematics and Statistics, Boston University, 111 Cumminton St., Boston, MA 02215, United States (email)
Krešimir Josić - Department of Mathematics and Statistics, Boston University, 111 Cumminton St., Boston, MA 02215, United States (email)
Monica Moreno-Rocha - Department of Mathematics and Statistics, Boston University, 111 Cumminton St., Boston, MA 02215, United States (email)

Abstract: 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.

Keywords:  Accessibility, cantor bouquets, Julia sets.
Mathematics Subject Classification:  37F50.

Received: February 2001;      Revised: May 2001;      Published: May 2001.