Abstract:In this paper we study rational functions of the form Rn,a,c(z) = z n + a z n + c and hold either a or c fixed while the other varies. We show that for certain ranges of a, the c-parameter plane contains homeomorphic copies of the Mandelbrot set, as well as the a-plane for certain ranges of c.We use techniques first introduced by Douady and Hubbard in [1] that were applied for the subfamily Rn,a,0 by Robert Devaney in [2]. These techniques involve polynomial-like maps of degree two.
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.