Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 3-22

SIERPINSKI CURVE JULIA SETS FOR QUADRATIC RATIONAL MAPS

Robert L. Devaney, Núria Fagella, Antonio Garijo and Xavier Jarque

Boston University, Department of Mathematics
111 Cummington Street, Boston, MA 02215, U.S.A.; bob 'at' bu.edu

Universitat de Barcelona, Departament de Matemātica Aplicada i Anālisi
Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain; fagella 'at' maia.ub.es

Universitat Rovira i Virgili, Departament d'Enginyeria Informātica i Matemātiques
Av. Paīsos Catalans 26, Tarragona 43007, Spain; antonio.garijo 'at' urv.cat

Universitat de Barcelona, Departament de Matemātica Aplicada i Anālisi
Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain; xavier.jarque 'at' ub.edu

Abstract. We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpinski curve.

2010 Mathematics Subject Classification: Primary 37F10, 37F15, 37F20, 37F45.

Key words: Iteration, Fatou and Julia sets, quadratic rational maps, Sierpinski curves.

Reference to this article: R.L. Devaney, N. Fagella, A. Garijo and X. Jarque: Sierpinski curve Julia sets for quadratic rational maps. Ann. Acad. Sci. Fenn. Math. 39 (2014), 3-22.

Full document as PDF file

doi:10.5186/aasfm.2014.3903