Name: On a Generalized Fatou-Julia Theorem
Creator: Dominic Rochon
Keywords: 0103 physical sciences, Julia sets, Cantor sets, Iteration theory, iterative and composite equations, Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables, Small divisors, rotation domains and linearization in holomorphic dynamics, 0101 mathematics, Bicomplex numbers, 01 natural sciences, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets

On a generalized Fatou-Julia theorem.

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 2003 English Publisher:World Scientific Pub Co Pte LtJournal:Fractals, volume 11, pages 213-219 (issn: 0218-348X, eissn: 1793-6543,

Authors: Dominic Rochon;

doi: 10.1142/s0218348x03002075

On a Generalized Fatou-Julia Theorem

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Abstract

In this article, we continue to explore some specific results in bicomplex dynamics. In particular, we give a bicomplex version of the so-called Fatou-Julia theorem. In fact, we give a complete topological characterization in ℝ4 of the bicomplex filled-Julia set for a quadratic polynomial in bicomplex numbers of the form w2 + c.

Related Organizations

Université du Québec à Trois-Rivières
Canada
University of Quebec
Canada

Keywords

Julia sets, Cantor sets, Iteration theory, iterative and composite equations, Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables, Small divisors, rotation domains and linearization in holomorphic dynamics, Bicomplex numbers, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets

4 Research products, page 1 of 1

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