Local connectivity of the Julia set of real polynomials

Genadi Levin; Sebastian Van Strien

doi:10.2307/120958

Local connectivity of the Julia set of real polynomials

Genadi Levin, Sebastian Van Strien

Einstein Institute of Mathematics

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

63 Scopus citations

Abstract

In this paper we shall show that the Julia set of real polynomials of the form f(z) = z^ℓ + c₁ with ℓ an even integer and c₁ real is either totally disconnected or locally connected. This answers a question of J. Milnor.

Original language	English
Pages (from-to)	471-541
Number of pages	71
Journal	Annals of Mathematics
Volume	147
Issue number	3
DOIs	https://doi.org/10.2307/120958
State	Published - May 1998

Access to Document

10.2307/120958

Cite this

@article{fa043d44501d4102b665dabdaaac0a7d,

title = "Local connectivity of the Julia set of real polynomials",

abstract = "In this paper we shall show that the Julia set of real polynomials of the form f(z) = zℓ + c1 with ℓ an even integer and c1 real is either totally disconnected or locally connected. This answers a question of J. Milnor.",

author = "Genadi Levin and {Van Strien}, Sebastian",

year = "1998",

month = may,

doi = "10.2307/120958",

language = "אנגלית",

volume = "147",

pages = "471--541",

journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Department of Mathematics at Princeton University",

number = "3",

}

TY - JOUR

T1 - Local connectivity of the Julia set of real polynomials

AU - Levin, Genadi

AU - Van Strien, Sebastian

PY - 1998/5

Y1 - 1998/5

N2 - In this paper we shall show that the Julia set of real polynomials of the form f(z) = zℓ + c1 with ℓ an even integer and c1 real is either totally disconnected or locally connected. This answers a question of J. Milnor.

AB - In this paper we shall show that the Julia set of real polynomials of the form f(z) = zℓ + c1 with ℓ an even integer and c1 real is either totally disconnected or locally connected. This answers a question of J. Milnor.

UR - http://www.scopus.com/inward/record.url?scp=0032333133&partnerID=8YFLogxK

U2 - 10.2307/120958

DO - 10.2307/120958

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0032333133

SN - 0003-486X

VL - 147

SP - 471

EP - 541

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 3

ER -

Local connectivity of the Julia set of real polynomials

Abstract

Access to Document

Other files and links

Fingerprint

Cite this