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On Fibonacci polynomials and wandering domains
Author(s) -
Trucco Eugenio
Publication year - 2015
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdv046
Subject(s) - mathematics , fibonacci number , julia set , ramification , combinatorics , polynomial , component (thermodynamics) , pure mathematics , discrete mathematics , mathematical analysis , physics , thermodynamics
It is known that in the complex case the Fatou set of a polynomial has no wandering components. This is not true in the non‐Archimedean case; there exist examples of polynomials having a wandering Fatou component. These examples are related to a phenomenon called wild ramification , a property that does not occur in the complex numbers. In this work, we will use combinatorics related to the Fibonacci numbers in order to obtain polynomials having a wandering Fatou component in the absence of the wild ramification phenomenon.