2005/03/30 by Gabriela Fernandez Lamilla, Lamilla, Gabriela Fernandez · 1 citation
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #advanced mathematical theories #math.DS
paper · pdf · doi:10.48550/arxiv.math/0503720
27 pages
arxiv created 2005/03/30 · openalex publication_date 2005/03/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We will study perturbations of the polynomials Pλ, of the form Qλ= Pλ+Q in the space of centered monic polynomials, where Pλ is the polynomial family defined by Pλ(z)=\fracλpzp+(1-\fracλp) z p+1 with λ∈ Λ= \z: |z-1| <1\, studied by Benedetto, who showed that for a dense set of parameters, the polynomials Pλ have a wandering disc contained in the filled Julia set. We will show an analogous result for the family Qλ, obtaining the following consequence: The polynomials Pλ belong to Ep+1 where Ep+1 denotes the set of polynomials that have a wandering disc in the filled Julia set, in the space of centered monic polynomials of degree p+1.