On Fibonacci polynomials and wandering domains | Zendy

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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.

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