Geometric Limits of Julia Sets of Maps z^n + exp(2πiθ) as n → ∞

Scott R. Kaschner; Reaper Romero; David Simmons

doi:10.1142/S0218127415300219

Geometric Limits of Julia Sets of Maps z^n + exp(2πiθ) as n → ∞

Scott R. Kaschner, Reaper Romero, David Simmons

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the geometric limit as n → ∞ of the Julia sets J(P _n,c ) for the maps P _n,c (z) = z ⁿ + c does not exist for almost every c on the unit circle. Furthermore, we show that there is always a subsequence along which the limit does exist and equals the unit circle.

Original language	American English
Journal	Scholarship and Professional Work - LAS
Volume	25
Issue number	8
DOIs	https://doi.org/10.1142/S0218127415300219
State	Published - Jan 1 2015

Keywords

complex dynamics
geometric limits
unicritical

Disciplines

Dynamical Systems
Mathematics

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10.1142/S0218127415300219License: Unspecified

Geometric Limits of Julia Sets of Maps z n exp(2 i ) as n Final published version, 936 KBLicense: Unspecified

Cite this

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title = "Geometric Limits of Julia Sets of Maps z\textasciicircum{}n + exp(2πiθ) as n → ∞",

abstract = " We show that the geometric limit as n → ∞ of the Julia sets J(P n,c ) for the maps P n,c (z) = z n + c does not exist for almost every c on the unit circle. Furthermore, we show that there is always a subsequence along which the limit does exist and equals the unit circle.",

keywords = "complex dynamics, geometric limits, unicritical",

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AU - Kaschner, Scott R.

AU - Romero, Reaper

AU - Simmons, David

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We show that the geometric limit as n → ∞ of the Julia sets J(P n,c ) for the maps P n,c (z) = z n + c does not exist for almost every c on the unit circle. Furthermore, we show that there is always a subsequence along which the limit does exist and equals the unit circle.

AB - We show that the geometric limit as n → ∞ of the Julia sets J(P n,c ) for the maps P n,c (z) = z n + c does not exist for almost every c on the unit circle. Furthermore, we show that there is always a subsequence along which the limit does exist and equals the unit circle.

KW - complex dynamics

KW - geometric limits

KW - unicritical

UR - https://digitalcommons.butler.edu/facsch_papers/858

U2 - 10.1142/S0218127415300219

DO - 10.1142/S0218127415300219

M3 - Article

VL - 25

JO - Scholarship and Professional Work - LAS

JF - Scholarship and Professional Work - LAS

IS - 8

ER -

Geometric Limits of Julia Sets of Maps z^n + exp(2πiθ) as n → ∞

Abstract

Keywords

Disciplines

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