Accessible points in the Julia sets of stable exponentials

Ranjit Bhattacharjee; Robert L. Devaney; R.E. Lee Deville; Krešimir Josić; Monica Moreno-Rocha

doi:10.3934/dcdsb.2001.1.299

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2001, Volume 1, Issue 3: 299-318. Doi: 10.3934/dcdsb.2001.1.299

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Accessible points in the Julia sets of stable exponentials

1.
Department of Mathematics and Statistics, Boston University, 111 Cumminton St., Boston, MA 02215
2.
Department of Mathematics and Statistics, Boston University, 111 Cummington St., Boston, MA 02215

Received: February 2001

Revised: May 2001

Published: August 2001

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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.

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Mathematics Subject Classification: 37F50.

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