On polynomials sharing preimages of compact sets, and related questions

Fedor Pakovich

doi:10.1007/s00039-007-0638-3

On polynomials sharing preimages of compact sets, and related questions

Fedor Pakovich

Department of Mathematics

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

18 Scopus citations

Abstract

In this paper we give a solution of the following problem: under what conditions on infinite compact sets K₁, K₂ ⊂ C and polynomials f ₁, f ₂ do the preimages f ₁ ^-1 {K ₁} and f ₂ ^-1 {K ₂} coincide. Besides, we investigate some related questions. In particular, we show that polynomials sharing an invariant compact set distinct from a point have equal Julia sets.

Original language	English
Pages (from-to)	163-183
Number of pages	21
Journal	Geometric and Functional Analysis
Volume	18
Issue number	1
DOIs	https://doi.org/10.1007/s00039-007-0638-3
State	Published - 1 Apr 2008

Keywords

Commuting polynomials
Julia sets
Ritt's theorems

ASJC Scopus subject areas

Analysis
Geometry and Topology

Access to Document

10.1007/s00039-007-0638-3

Cite this

@article{573e0b601baa48ca86573847910acbd8,

title = "On polynomials sharing preimages of compact sets, and related questions",

abstract = "In this paper we give a solution of the following problem: under what conditions on infinite compact sets K1, K2 ⊂ C and polynomials f 1, f 2 do the preimages f 1 -1 {K 1} and f 2 -1 {K 2} coincide. Besides, we investigate some related questions. In particular, we show that polynomials sharing an invariant compact set distinct from a point have equal Julia sets.",

keywords = "Commuting polynomials, Julia sets, Ritt's theorems",

author = "Fedor Pakovich",

note = "Funding Information: Keywords and phrases: Julia sets, commuting polynomials, Ritt{\textquoteright}s theorems AMS Mathematics Subject Classification: 30D05, 37F10 Research supported by the ISF, Grant No. 979/05.",

year = "2008",

month = apr,

day = "1",

doi = "10.1007/s00039-007-0638-3",

language = "English",

volume = "18",

pages = "163--183",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Birkhauser Verlag Basel",

number = "1",

}

TY - JOUR

T1 - On polynomials sharing preimages of compact sets, and related questions

AU - Pakovich, Fedor

N1 - Funding Information: Keywords and phrases: Julia sets, commuting polynomials, Ritt’s theorems AMS Mathematics Subject Classification: 30D05, 37F10 Research supported by the ISF, Grant No. 979/05.

PY - 2008/4/1

Y1 - 2008/4/1

N2 - In this paper we give a solution of the following problem: under what conditions on infinite compact sets K1, K2 ⊂ C and polynomials f 1, f 2 do the preimages f 1 -1 {K 1} and f 2 -1 {K 2} coincide. Besides, we investigate some related questions. In particular, we show that polynomials sharing an invariant compact set distinct from a point have equal Julia sets.

AB - In this paper we give a solution of the following problem: under what conditions on infinite compact sets K1, K2 ⊂ C and polynomials f 1, f 2 do the preimages f 1 -1 {K 1} and f 2 -1 {K 2} coincide. Besides, we investigate some related questions. In particular, we show that polynomials sharing an invariant compact set distinct from a point have equal Julia sets.

KW - Commuting polynomials

KW - Julia sets

KW - Ritt's theorems

UR - http://www.scopus.com/inward/record.url?scp=42749088714&partnerID=8YFLogxK

U2 - 10.1007/s00039-007-0638-3

DO - 10.1007/s00039-007-0638-3

M3 - Article

AN - SCOPUS:42749088714

SN - 1016-443X

VL - 18

SP - 163

EP - 183

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 1

ER -

On polynomials sharing preimages of compact sets, and related questions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this