Abstract
Let Q(z) = znP(z) − zdeg PP(z−1), where P is the minimal polynomial of a Pisot number. Boyd [Duke Math. J. 44 (1977), 315–328] showed that, for (Formula presented.), Q is the product of cyclotomic polynomials and the minimal polynomial of a Salem number, say α. In this paper, we study the dynamics of the Newton map N = z − Q/Q′ induced by Q in the immediate basin Uα of α. We establish that N is a 2-fold covering map of Uα onto itself. Furthermore, there exists a conformal mapping φ of Uα onto the open unit disk D such that (Formula presented.) for all z∈D.
Original language | English (US) |
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Pages (from-to) | 371-378 |
Number of pages | 8 |
Journal | Journal of Fixed Point Theory and Applications |
Volume | 17 |
Issue number | 2 |
DOIs | |
State | Published - Jun 23 2015 |
Keywords
- Primary 37F10
- Secondary 11R06
ASJC Scopus subject areas
- Modeling and Simulation
- Geometry and Topology
- Applied Mathematics